What is the derivative of {f}(x(x)^n) ?

The derivative of {f}(x(x)^n) is derivative of {f}(x)x^n+nx^{n-1}{f}(x)

What is the first derivative of {f}(x(x)^n) ?

The first derivative of {f}(x(x)^n) is derivative of {f}(x)x^n+nx^{n-1}{f}(x)

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\frac{d}{d x} (f (x) (x)^{n})

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

Solution steps

\frac{d}{d x} (f (x) (x)^{n})

Apply the Product Rule:

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

f = f (x), g = x^{n}

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

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

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

\int \frac{x ^{5} - x ^{3} + 6 x}{x ^{4}} d x

\frac{d}{d x} (sin (3 x^{3} + 2))

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

\int_{2}^{\infty} e^{- 8 p} d p

n = 1 \sum \infty (\frac{5}{9})^{n}

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