What is the derivative of ((-2x-3^7)/((4x+2)^4)) ?

The derivative of ((-2x-3^7)/((4x+2)^4)) is -((-2x-3)^6(6x-5))/(8(2x+1)^5)

What is the first derivative of ((-2x-3^7)/((4x+2)^4)) ?

The first derivative of ((-2x-3^7)/((4x+2)^4)) is -((-2x-3)^6(6x-5))/(8(2x+1)^5)

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\frac{d}{d x} (\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}})

- \frac{( - 2 x - 3 ) ^{6} ( 6 x - 5 )}{8 ( 2 x + 1 ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( - 2 x - 3 ) ^{7} ) ( 4 x + 2 ) ^{4} - \frac{d}{d x} ( ( 4 x + 2 ) ^{4} ) ( - 2 x - 3 ) ^{7}}{( ( 4 x + 2 ) ^{4} ) ^{2}}

\frac{d}{d x} ((- 2 x - 3)^{7}) = - 14 (- 2 x - 3)^{6}

\frac{d}{d x} ((4 x + 2)^{4}) = 16 (4 x + 2)^{3}

= \frac{( - 14 ( - 2 x - 3 ) ^{6} ) ( 4 x + 2 ) ^{4} - 16 ( 4 x + 2 ) ^{3} ( - 2 x - 3 ) ^{7}}{( ( 4 x + 2 ) ^{4} ) ^{2}}

Simplify

\frac{( - 14 ( - 2 x - 3 ) ^{6} ) ( 4 x + 2 ) ^{4} - 16 ( 4 x + 2 ) ^{3} ( - 2 x - 3 ) ^{7}}{( ( 4 x + 2 ) ^{4} ) ^{2}} : - \frac{( - 2 x - 3 ) ^{6} ( 6 x - 5 )}{8 ( 2 x + 1 ) ^{5}}

= - \frac{( - 2 x - 3 ) ^{6} ( 6 x - 5 )}{8 ( 2 x + 1 ) ^{5}}

2 - 2 x^{2}

\int \frac{y}{( y ^{2} + 1 ) ^{2}} d y

n = 0 \sum \infty \frac{2 n}{3 n + 1}

y^{^{'}} = \frac{y}{t} + 1

\frac{d x}{d t} = x (1 - 0.0008 x)

What is the derivative of ((-2x-3^7)/((4x+2)^4)) ?
The derivative of ((-2x-3^7)/((4x+2)^4)) is -((-2x-3)^6(6x-5))/(8(2x+1)^5)
What is the first derivative of ((-2x-3^7)/((4x+2)^4)) ?
The first derivative of ((-2x-3^7)/((4x+2)^4)) is -((-2x-3)^6(6x-5))/(8(2x+1)^5)