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Popular >

derivative of y=(2x+1)+2/((2x+1)^3)

Solution

derivative of

y = (2 x + 1) + \frac{2}{( 2 x + 1 ) ^{3}}

Solution

- \frac{12}{( 2 x + 1 ) ^{4}} + 2

Solution steps

\frac{d}{d x} ((2 x + 1) + \frac{2}{( 2 x + 1 ) ^{3}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x) + \frac{d}{d x} (1) + \frac{d}{d x} (\frac{2}{( 2 x + 1 ) ^{3}})

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

\frac{d}{d x} (1) = 0

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

= 2 + 0 - \frac{12}{( 2 x + 1 ) ^{4}}

Simplify

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

Popular Examples

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\int_{- 1}^{1} x (1 - x)^{2} d x

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x \to 0 + lim (\frac{1}{sin ^{2} ( x )})

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\int \frac{x ^{2} ln ( x )}{2} d x

sum from n=0 to infinity of (n^2)/(e^n)

n = 0 \sum \infty \frac{n ^{2}}{e ^{n}}

Frequently Asked Questions (FAQ)

What is the derivative of y=(2x+1)+2/((2x+1)^3) ?
The derivative of y=(2x+1)+2/((2x+1)^3) is -(12)/((2x+1)^4)+2
What is the first derivative of y=(2x+1)+2/((2x+1)^3) ?
The first derivative of y=(2x+1)+2/((2x+1)^3) is -(12)/((2x+1)^4)+2