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Popular >

derivative of f(x)=(-9x^3+2x^2)^5

Solution

derivative of

f (x) = (- 9 x^{3} + 2 x^{2})^{5}

Solution

5 (- 9 x^{3} + 2 x^{2})^{4} (- 27 x^{2} + 4 x)

Solution steps

\frac{d}{d x} ((- 9 x^{3} + 2 x^{2})^{5})

Apply the chain rule:

5 (- 9 x^{3} + 2 x^{2})^{4} \frac{d}{d x} (- 9 x^{3} + 2 x^{2})

= 5 (- 9 x^{3} + 2 x^{2})^{4} \frac{d}{d x} (- 9 x^{3} + 2 x^{2})

\frac{d}{d x} (- 9 x^{3} + 2 x^{2}) = - 27 x^{2} + 4 x

= 5 (- 9 x^{3} + 2 x^{2})^{4} (- 27 x^{2} + 4 x)

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(-9x^3+2x^2)^5 ?
The derivative of f(x)=(-9x^3+2x^2)^5 is 5(-9x^3+2x^2)^4(-27x^2+4x)
What is the first derivative of f(x)=(-9x^3+2x^2)^5 ?
The first derivative of f(x)=(-9x^3+2x^2)^5 is 5(-9x^3+2x^2)^4(-27x^2+4x)