What is the derivative of (2x^5+8/(x^3)) ?

The derivative of (2x^5+8/(x^3)) is (4(x^5-6))/(x^4)

What is the first derivative of (2x^5+8/(x^3)) ?

The first derivative of (2x^5+8/(x^3)) is (4(x^5-6))/(x^4)

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\frac{d}{d x} (\frac{2 x ^{5} + 8}{x ^{3}})

\frac{4 ( x ^{5} - 6 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{5} + 8}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{5} + 8 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 2 x ^{5} + 8 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (2 x^{5} + 8) = 10 x^{4}

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

= \frac{10 x ^{4} x ^{3} - 3 x ^{2} ( 2 x ^{5} + 8 )}{( x ^{3} ) ^{2}}

Simplify

\frac{10 x ^{4} x ^{3} - 3 x ^{2} ( 2 x ^{5} + 8 )}{( x ^{3} ) ^{2}} : \frac{4 ( x ^{5} - 6 )}{x ^{4}}

= \frac{4 ( x ^{5} - 6 )}{x ^{4}}

15 x ln (14 x)

n = 2 \sum \infty \frac{3 n}{n ^{2} - 2}

x \to 5 + lim (\frac{6 x}{x - 5})

\int 3 x 5 x^{2} + 1 d x

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

What is the derivative of (2x^5+8/(x^3)) ?
The derivative of (2x^5+8/(x^3)) is (4(x^5-6))/(x^4)
What is the first derivative of (2x^5+8/(x^3)) ?
The first derivative of (2x^5+8/(x^3)) is (4(x^5-6))/(x^4)