What is the derivative of g(x)=sqrt(x)(x^3-x) ?

The derivative of g(x)=sqrt(x)(x^3-x) is (7x^2sqrt(x)-3sqrt(x))/2

What is the first derivative of g(x)=sqrt(x)(x^3-x) ?

The first derivative of g(x)=sqrt(x)(x^3-x) is (7x^2sqrt(x)-3sqrt(x))/2

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derivative of

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

\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_{0}^{\frac{π}{2}} cos^{6} (x) d x

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