Or press and hold the picture and choose “Save image”.
for Whoobee's shop
Derivatives: The Power Rule — Easy Worksheet 1
Grade 12 · MathSheets Name: ____________________ Date: __________
Find f'(x) — write just the expression, like 6x^2 - 4 — or the number asked for.
How to solve
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Example
Find f'(x) for f(x) = 6x³.
Answer: 18x²
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(x5) = 1 × 5x4 = 5x4. So f'(x) = 5x4.
✓ Correct!
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(x5) = 1 × 5x4 = 5x4. So f'(x) = 5x4.
💡 How to solve: Derivatives: The Power Rule
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Try a similar one
Find f'(x) for f(x) = 3x².
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-6x4) = -6 × 4x³ = -24x³. So f'(x) = -24x³.
✓ Correct!
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-6x4) = -6 × 4x³ = -24x³. So f'(x) = -24x³.
💡 How to solve: Derivatives: The Power Rule
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Try a similar one
Find f'(x) for f(x) = 8x4.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-8x²) = -8 × 2x = -16x. So f'(x) = -16x.
✓ Correct!
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-8x²) = -8 × 2x = -16x. So f'(x) = -16x.
💡 How to solve: Derivatives: The Power Rule
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Try a similar one
Find f'(x) for f(x) = 5x².
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-2x6) = -2 × 6x5 = -12x5. So f'(x) = -12x5.
✓ Correct!
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-2x6) = -2 × 6x5 = -12x5. So f'(x) = -12x5.
💡 How to solve: Derivatives: The Power Rule
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Try a similar one
Find f'(x) for f(x) = -x4.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-5x³) = -5 × 3x² = -15x². So f'(x) = -15x².
✓ Correct!
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-5x³) = -5 × 3x² = -15x². So f'(x) = -15x².
💡 How to solve: Derivatives: The Power Rule
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Try a similar one
Find f'(x) for f(x) = 3x³.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(6x³) = 6 × 3x² = 18x². So f'(x) = 18x².
✓ Correct!
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(6x³) = 6 × 3x² = 18x². So f'(x) = 18x².
💡 How to solve: Derivatives: The Power Rule
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Try a similar one
Find f'(x) for f(x) = -9x².
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-9x²) = -9 × 2x = -18x. So f'(x) = -18x.
✓ Correct!
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(-9x²) = -9 × 2x = -18x. So f'(x) = -18x.
💡 How to solve: Derivatives: The Power Rule
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Try a similar one
Find f'(x) for f(x) = 3x².
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(8x4) = 8 × 4x³ = 32x³. So f'(x) = 32x³.
✓ Correct!
Not quite. The answer is
💡 Use the power rule d/dx(axn) = (a × n)xn−1 on each term: d/dx(8x4) = 8 × 4x³ = 32x³. So f'(x) = 32x³.
💡 How to solve: Derivatives: The Power Rule
Power rule: the derivative of axn is (a·n)xn-1. Differentiate term by term; a constant term has derivative 0. To find f'(a), differentiate first, then substitute x = a.
Try a similar one
Find f'(x) for f(x) = -9x².
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Log in to save your progress.
Derivatives: The Power Rule — Easy Worksheet 1
Find f'(x) — write just the expression, like 6x^2 - 4 — or the number asked for.