What is the derivative of f(x)=(x^4+5x^2+10)/(x^2) ?

The derivative of f(x)=(x^4+5x^2+10)/(x^2) is (2(x^4-10))/(x^3)

What is the first derivative of f(x)=(x^4+5x^2+10)/(x^2) ?

The first derivative of f(x)=(x^4+5x^2+10)/(x^2) is (2(x^4-10))/(x^3)

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derivative of

f (x) = \frac{x ^{4} + 5 x ^{2} + 10}{x ^{2}}

\frac{2 ( x ^{4} - 10 )}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{4} + 5 x ^{2} + 10}{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} + 5 x ^{2} + 10 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{4} + 5 x ^{2} + 10 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{4} + 5 x^{2} + 10) = 4 x^{3} + 10 x

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

= \frac{( 4 x ^{3} + 10 x ) x ^{2} - 2 x ( x ^{4} + 5 x ^{2} + 10 )}{( x ^{2} ) ^{2}}

Simplify

\frac{( 4 x ^{3} + 10 x ) x ^{2} - 2 x ( x ^{4} + 5 x ^{2} + 10 )}{( x ^{2} ) ^{2}} : \frac{2 ( x ^{4} - 10 )}{x ^{3}}

= \frac{2 ( x ^{4} - 10 )}{x ^{3}}

\int e^{x} - e^{- x} d x

x = 1 - y^{2}, x = y^{2} - 1

\frac{\partial}{\partial x} (\frac{h ( x ) c}{x})

\int \frac{1}{4 x ( 3 + x )} d x

\int \frac{7 x}{x - 1} d x

What is the derivative of f(x)=(x^4+5x^2+10)/(x^2) ?
The derivative of f(x)=(x^4+5x^2+10)/(x^2) is (2(x^4-10))/(x^3)
What is the first derivative of f(x)=(x^4+5x^2+10)/(x^2) ?
The first derivative of f(x)=(x^4+5x^2+10)/(x^2) is (2(x^4-10))/(x^3)