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Popular Calculus >

derivative of (4x^3+5/x)

Solution

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

Solution

\frac{8 x ^{3} - 5}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 x^{3} + 5) = 12 x^{2}

\frac{d x}{d x} = 1

= \frac{12 x ^{2} x - 1 \cdot ( 4 x ^{3} + 5 )}{x ^{2}}

Simplify

\frac{12 x ^{2} x - 1 \cdot ( 4 x ^{3} + 5 )}{x ^{2}} : \frac{8 x ^{3} - 5}{x ^{2}}

= \frac{8 x ^{3} - 5}{x ^{2}}

Graph

Popular Examples

derivative of g(x)=(1-3t)/(6+t)

d er i v a t i v e g (x) = \frac{1 - 3 t}{6 + t}

(dy)/(dx)+4x^3y=x^3

\frac{d y}{d x} + 4 x^{3} y = x^{3}

integral of (41)/(x^3-125)

\int \frac{41}{x ^{3} - 125} d x

integral of (ln(15x))/x

\int \frac{ln ( 15 x )}{x} d x

integral of (x^3+2x^2-4)/(x^2)

\int \frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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