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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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