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Popular >

derivative of 1/(2x^2+(x^4)/(16))

Solution

\frac{d}{d x} (\frac{1}{2 x ^{2}} + \frac{x ^{4}}{16})

Solution

- \frac{1}{x ^{3}} + \frac{x ^{3}}{4}

Solution steps

\frac{d}{d x} (\frac{1}{2 x ^{2}} + \frac{x ^{4}}{16})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{2 x ^{2}}) + \frac{d}{d x} (\frac{x ^{4}}{16})

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

\frac{d}{d x} (\frac{x ^{4}}{16}) = \frac{x ^{3}}{4}

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

Popular Examples

derivative of (x^2-sqrt(x)+3/4 x^4^2)

\frac{d}{d x} ((x^{2} - x + \frac{3}{4} x^{4})^{2})

y^'=(6x^2+y^2)/(xy)

y^{^{'}} = \frac{6 x ^{2} + y ^{2}}{x y}

integral of ye^{xy}

\int y e^{x y} d x

integral of xsqrt(5x+1)

\int x 5 x + 1 d x

y^'=((e^{x-y}))/(1+e^x),y(1)=0

y^{^{'}} = \frac{( e ^{x - y} )}{1 + e ^{x}}, y (1) = 0

Frequently Asked Questions (FAQ)

What is the derivative of 1/(2x^2+(x^4)/(16)) ?
The derivative of 1/(2x^2+(x^4)/(16)) is -1/(x^3)+(x^3)/4
What is the first derivative of 1/(2x^2+(x^4)/(16)) ?
The first derivative of 1/(2x^2+(x^4)/(16)) is -1/(x^3)+(x^3)/4