What is the derivative of sqrt(x^3)-1/(x^7) ?

The derivative of sqrt(x^3)-1/(x^7) is (3sqrt(x))/2+7/(x^8)

What is the first derivative of sqrt(x^3)-1/(x^7) ?

The first derivative of sqrt(x^3)-1/(x^7) is (3sqrt(x))/2+7/(x^8)

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\frac{d}{d x} (x^{3} - \frac{1}{x ^{7}})

\frac{3 x}{2} + \frac{7}{x ^{8}}

Solution steps

\frac{d}{d x} (x^{3} - \frac{1}{x ^{7}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (\frac{1}{x ^{7}})

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

\frac{d}{d x} (\frac{1}{x ^{7}}) = - \frac{7}{x ^{8}}

= \frac{3 x}{2} - (- \frac{7}{x ^{8}})

Simplify

= \frac{3 x}{2} + \frac{7}{x ^{8}}

What is the derivative of sqrt(x^3)-1/(x^7) ?
The derivative of sqrt(x^3)-1/(x^7) is (3sqrt(x))/2+7/(x^8)
What is the first derivative of sqrt(x^3)-1/(x^7) ?
The first derivative of sqrt(x^3)-1/(x^7) is (3sqrt(x))/2+7/(x^8)