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Popular >

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

Solution

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

Solution

f (x) + x \frac{d}{d x} (f (x))

Solution steps

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

Simplify

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

= \frac{d}{d x} (x f (x))

Apply the Product Rule:

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

f = x, g = f (x)

= \frac{d x}{d x} f (x) + \frac{d}{d x} (f (x)) x

\frac{d x}{d x} = 1

= 1 \cdot f (x) + \frac{d}{d x} (f (x)) x

Simplify

= f (x) + x \frac{d}{d x} (f (x))

Popular Examples

integral of sin(x)*tan(x)

\int sin (x) \cdot tan (x) d x

integral from 0 to 1 of pi(5x^2)^2

\int_{0}^{1} π (5 x^{2})^{2} d x

integral of x-csc(x)cot(x)

\int x - csc (x) cot (x) d x

integral of (sin(7x))

\int (sin (7 x)) d x

derivative of 1/2 ln(2x)

\frac{d}{d x} (\frac{1}{2} ln (2 x))

Frequently Asked Questions (FAQ)

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