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

The derivative of f(x^2(x)) is 3x^2{f}(x)+derivative of {f}(x)x^3

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

The first derivative of f(x^2(x)) is 3x^2{f}(x)+derivative of {f}(x)x^3

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

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

Solution steps

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

Simplify

f (x) (x)^{2} (x) : x^{3} f (x)

= \frac{d}{d x} (x^{3} f (x))

Apply the Product Rule:

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

f = x^{3}, g = f (x)

= \frac{d}{d x} (x^{3}) f (x) + \frac{d}{d x} (f (x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

What is the derivative of f(x^2(x)) ?
The derivative of f(x^2(x)) is 3x^2{f}(x)+derivative of {f}(x)x^3
What is the first derivative of f(x^2(x)) ?
The first derivative of f(x^2(x)) is 3x^2{f}(x)+derivative of {f}(x)x^3