What is the derivative of {f}(x(x^3)) ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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