Chain rule
Differentiate a power of a linear expression using the chain rule. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Differentiate f(x) using the chain rule.
f(x) = (x + 4)2
- 4(x + 4)
- −2(x + 4)
- 2(x + 4)2
- 2(x + 4)
Answer: 2(x + 4)
See one solved, step by step
Differentiate f(x) using the chain rule.
f(x) = (2x - 3)2
- −4(2x - 3)
- 2(2x - 3)
- 4(2x - 3)
- 4(2x - 3)2
📘 Worked solution
1Outer: d/dx[(...)2] = 2(...)1Treat the bracket as a single block and apply the power rule to it.
2Inner: d/dx[2x - 3] = 2The derivative of the inside expression 2x - 3 is just its slope, 2.
3f'(x) = 2(2x - 3)1 · 2 = 4(2x - 3)Chain rule multiplies the outer derivative by the inner derivative.
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