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Popular >

derivative of (3x^3+7)/x

Solution

derivative of

\frac{3 x ^{3} + 7}{x}

Solution

\frac{6 x ^{3} - 7}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{3} + 7}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x ^{3} + 7 ) x - \frac{d x}{d x} ( 3 x ^{3} + 7 )}{x ^{2}}

\frac{d}{d x} (3 x^{3} + 7) = 9 x^{2}

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

= \frac{9 x ^{2} x - 1 \cdot ( 3 x ^{3} + 7 )}{x ^{2}}

Simplify

\frac{9 x ^{2} x - 1 \cdot ( 3 x ^{3} + 7 )}{x ^{2}} : \frac{6 x ^{3} - 7}{x ^{2}}

= \frac{6 x ^{3} - 7}{x ^{2}}

Popular Examples

derivative of (3x-1^4)

\frac{d}{d x} ((3 x - 1)^{4})

derivative of-cos(2x-sin(2x)-1/5 e^x)

\frac{d}{d x} (- cos (2 x) - sin (2 x) - \frac{1}{5} e^{x})

2(dy)/(dx)+6y=3

2 \frac{d y}{d x} + 6 y = 3

derivative of (2x^3-3x+2^4)

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

limit as x approaches 2-of (x+2)/(x-3)

x \to 2 - lim (\frac{x + 2}{x - 3})

Frequently Asked Questions (FAQ)

What is the derivative of (3x^3+7)/x ?
The derivative of (3x^3+7)/x is (6x^3-7)/(x^2)
What is the first derivative of (3x^3+7)/x ?
The first derivative of (3x^3+7)/x is (6x^3-7)/(x^2)