What is the derivative of f(x)=(x^5+4x)/(x^3) ?

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

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

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

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derivative of

f (x) = \frac{x ^{5} + 4 x}{x ^{3}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y^{^{'}} = (1 - y) \cdot sin (x)

\int_{2}^{3} \frac{18}{3 - x} d x

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

y^{^{''''}} + 2 y^{^{''}} + y = 0

e^{7 x}

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