What is the derivative of {f}(x(x^2)) ?

The derivative of {f}(x(x^2)) is derivative of {f}(x)x^2+2x{f}(x)

What is the first derivative of {f}(x(x^2)) ?

The first derivative of {f}(x(x^2)) is derivative of {f}(x)x^2+2x{f}(x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

\int \frac{5 - 50 x}{1 - 25 x ^{2}} d x

n = 0 \sum \infty 2 \cdot 6^{n}

\frac{d y}{d x} = \frac{( x - 4 )}{y + 5}

d er i v a t i v e \frac{t}{2 t + 3}

\int cos^{3} (4 θ) sin (4 θ) d θ

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