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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

Graph

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\int_{0}^{π} sin^{2} (n x) d x

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\int 3 (3 x + 9)^{7} d x

(\partial)/(\partial x)(6xyz-7xy^2z^3)

\frac{\partial}{\partial x} (6 x yz - 7 x y^{2} z^{3})

normal of f(x)=log_{2}(2x^2+14),\at x=5 normal of

f (x) = lo g_{2} (2 x^{2} + 14), at x = 5

(dx)/(dt)=2+2x+t+tx

\frac{d x}{d t} = 2 + 2 x + t + t x

Frequently Asked Questions (FAQ)

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