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Popular >

derivative of sqrt(x^3)-1/(x^7)

Solution

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

Solution

\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}}

Popular Examples

(dy)/(dx)-e^{x+y}=0

\frac{d y}{d x} - e^{x + y} = 0

limit as x approaches infinity of (((4+x))/x)^{3+x/3}

x \to \infty lim ((\frac{( 4 + x )}{x})^{3 + \frac{x}{3}})

x^2-1xy+x(dy)/(dx)=0

x^{2} - 1 x y + x \frac{d y}{d x} = 0

integral of ln|x-2|

\int ln ∣ x - 2 ∣ d x

y^'=sqrt(yx),y(1)=7

y^{^{'}} = y x, y (1) = 7

Frequently Asked Questions (FAQ)

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)