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Popular >

derivative of f(x(1x^2-1))

Solution

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

Solution

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

Solution steps

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

Simplify

f (x) (1 \cdot x^{2} - 1) : f (x) (x^{2} - 1)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = f (x), g = x^{2} - 1

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

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of f(x(1x^2-1)) ?
The derivative of f(x(1x^2-1)) is derivative of {f}(x)(x^2-1)+2x{f}(x)
What is the first derivative of f(x(1x^2-1)) ?
The first derivative of f(x(1x^2-1)) is derivative of {f}(x)(x^2-1)+2x{f}(x)