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Popular >

derivative of f(x)=5(1-x^2)^9

Solution

derivative of

f (x) = 5 (1 - x^{2})^{9}

Solution

- 90 x (1 - x^{2})^{8}

Solution steps

\frac{d}{d x} (5 (1 - x^{2})^{9})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} ((1 - x^{2})^{9})

Apply the chain rule:

9 (1 - x^{2})^{8} \frac{d}{d x} (1 - x^{2})

= 9 (1 - x^{2})^{8} \frac{d}{d x} (1 - x^{2})

\frac{d}{d x} (1 - x^{2}) = - 2 x

= 5 \cdot 9 (1 - x^{2})^{8} (- 2 x)

Simplify

= - 90 x (1 - x^{2})^{8}

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=5(1-x^2)^9 ?
The derivative of f(x)=5(1-x^2)^9 is -90x(1-x^2)^8
What is the first derivative of f(x)=5(1-x^2)^9 ?
The first derivative of f(x)=5(1-x^2)^9 is -90x(1-x^2)^8