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Popular >

derivative of f(x(x^2-x))

Solution

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

Solution

\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)

Popular Examples

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y^{^{''}} - 2 y^{^{'}} + y = e^{x}

inverse oflaplace 8/((s-4)*(s+4)^2)inverse laplace

\frac{8}{( s - 4 ) \cdot ( s + 4 ) ^{2}}

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x \to 0 lim (\frac{( x ^{2} - 2 x )}{x})

(\partial)/(\partial x)(4ye^{5x})

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sum from n=0 to infinity of x/(2^n)

n = 0 \sum \infty \frac{x}{2 ^{n}}

Frequently Asked Questions (FAQ)

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)