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Popular >

derivative of sqrt(x)+1/(x^3)

Solution

\frac{d}{d x} (x + \frac{1}{x ^{3}})

Solution

\frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

Solution steps

\frac{d}{d x} (x + \frac{1}{x ^{3}})

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

= \frac{1}{2 x} - \frac{3}{x ^{4}}

Simplify

\frac{1}{2 x} - \frac{3}{x ^{4}} : \frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

= \frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

Popular Examples

(\partial)/(\partial x)(x^2+y^3)

\frac{\partial}{\partial x} (x^{2} + y^{3})

normal of h(x)=3e^x-7x,(0,3)normal of

h (x) = 3 e^{x} - 7 x, (0, 3)

inverse oflaplace 1/(2s+5)inverse laplace

\frac{1}{2 s + 5}

limit as x approaches+0 of cos^2(x)

x \to + 0 lim (cos^{2} (x))

limit as x approaches-infinity of-3

x \to - \infty lim (- 3)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)+1/(x^3) ?
The derivative of sqrt(x)+1/(x^3) is (x^{7/2}-6)/(2x^{7/2)sqrt(x)}
What is the first derivative of sqrt(x)+1/(x^3) ?
The first derivative of sqrt(x)+1/(x^3) is (x^{7/2}-6)/(2x^{7/2)sqrt(x)}