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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

Popular Examples

derivative of y=arccos(e^{3x})

d er i v a t i v e y = arccos (e^{3 x})

derivative of f(x)=x^3-3x^2-45x+5

d er i v a t i v e f (x) = x^{3} - 3 x^{2} - 45 x + 5

(1 - \frac{1}{x})^{^{'}}

y^{''}-3/t y^'+(20)/(t^2)y=0

y^{^{''}} - \frac{3}{t} y^{^{'}} + \frac{20}{t ^{2}} y = 0

derivative of arcsin(2x-3)

d er i v a t i v e arcsin (2 x - 3)

Frequently Asked Questions (FAQ)

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