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Popular >

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

Solution

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

Solution

- \frac{6}{( 2 x + 3 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{1}{2 x + 3})^{2} (- \frac{2}{( 2 x + 3 ) ^{2}}) : - \frac{6}{( 2 x + 3 ) ^{4}}

= - \frac{6}{( 2 x + 3 ) ^{4}}

Popular Examples

derivative of f(x)=arctan((1+x)/(1-x))derivative of

f (x) = arctan (\frac{1 + x}{1 - x})

(\partial)/(\partial x)(1+x^3+y^4)

\frac{\partial}{\partial x} (1 + x^{3} + y^{4})

integral of (3x+4)/(x+3)

\int \frac{3 x + 4}{x + 3} d x

integral from 0 to 1 of-10(x^2+1)e^{-x}

\int_{0}^{1} - 10 (x^{2} + 1) e^{- x} d x

(dy}{dx}=\frac{(x^2-y))/x

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

Frequently Asked Questions (FAQ)

What is the derivative of (1/(2x+3)^3) ?
The derivative of (1/(2x+3)^3) is -6/((2x+3)^4)
What is the first derivative of (1/(2x+3)^3) ?
The first derivative of (1/(2x+3)^3) is -6/((2x+3)^4)