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Popular >

derivative of f(x)=sqrt(x)(x^3-x)

Solution

derivative of

f (x) = x (x^{3} - x)

Solution

\frac{7 x ^{2} x - 3 x}{2}

Solution steps

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

Apply the Product Rule:

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

f = x, g = x^{3} - x

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

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

\frac{d}{d x} (x^{3} - x) = 3 x^{2} - 1

= \frac{1}{2 x} (x^{3} - x) + (3 x^{2} - 1) x

Simplify

\frac{1}{2 x} (x^{3} - x) + (3 x^{2} - 1) x : \frac{7 x ^{2} x - 3 x}{2}

= \frac{7 x ^{2} x - 3 x}{2}

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\int \frac{4 x - 11}{2 x ^{2} - 11 x + 15} d x

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\frac{\partial}{\partial y} (2 x + arctan (y^{2}))

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\int e^{\frac{5}{2} x} d x

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\int x cos (4 π x^{2}) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x)(x^3-x) ?
The derivative of f(x)=sqrt(x)(x^3-x) is (7x^2sqrt(x)-3sqrt(x))/2
What is the first derivative of f(x)=sqrt(x)(x^3-x) ?
The first derivative of f(x)=sqrt(x)(x^3-x) is (7x^2sqrt(x)-3sqrt(x))/2