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Popular >

derivative of (x^5+9/(x^3))

Solution

\frac{d}{d x} (\frac{x ^{5} + 9}{x ^{3}})

Solution

\frac{2 x ^{5} - 27}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{x ^{5} + 9}{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} + 9 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( x ^{5} + 9 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (x^{5} + 9) = 5 x^{4}

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

= \frac{5 x ^{4} x ^{3} - 3 x ^{2} ( x ^{5} + 9 )}{( x ^{3} ) ^{2}}

Simplify

\frac{5 x ^{4} x ^{3} - 3 x ^{2} ( x ^{5} + 9 )}{( x ^{3} ) ^{2}} : \frac{2 x ^{5} - 27}{x ^{4}}

= \frac{2 x ^{5} - 27}{x ^{4}}

Graph

Popular Examples

integral of 1/((x^2+a^2))

\int \frac{1}{( x ^{2} + a ^{2} )} d x

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

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y = sin (x), y = cos (x), x = 0, x = 2 π

derivative of e^{x^6}+log_{5}(pi)

\frac{d}{d x} (e^{x^{6}} + lo g_{5} (π))

(\partial)/(\partial x)(2x+3y-6)

\frac{\partial}{\partial x} (2 x + 3 y - 6)

Frequently Asked Questions (FAQ)

What is the derivative of (x^5+9/(x^3)) ?
The derivative of (x^5+9/(x^3)) is (2x^5-27)/(x^4)
What is the first derivative of (x^5+9/(x^3)) ?
The first derivative of (x^5+9/(x^3)) is (2x^5-27)/(x^4)