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

The derivative of ((2x+3^4)/((3x-2)^5)) is ((2x+3)^3(-6x-61))/((3x-2)^6)

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

The first derivative of ((2x+3^4)/((3x-2)^5)) is ((2x+3)^3(-6x-61))/((3x-2)^6)

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

\frac{( 2 x + 3 ) ^{3} ( - 6 x - 61 )}{( 3 x - 2 ) ^{6}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((2 x + 3)^{4}) = 8 (2 x + 3)^{3}

\frac{d}{d x} ((3 x - 2)^{5}) = 15 (3 x - 2)^{4}

= \frac{8 ( 2 x + 3 ) ^{3} ( 3 x - 2 ) ^{5} - 15 ( 3 x - 2 ) ^{4} ( 2 x + 3 ) ^{4}}{( ( 3 x - 2 ) ^{5} ) ^{2}}

Simplify

\frac{8 ( 2 x + 3 ) ^{3} ( 3 x - 2 ) ^{5} - 15 ( 3 x - 2 ) ^{4} ( 2 x + 3 ) ^{4}}{( ( 3 x - 2 ) ^{5} ) ^{2}} : \frac{( 2 x + 3 ) ^{3} ( - 6 x - 61 )}{( 3 x - 2 ) ^{6}}

= \frac{( 2 x + 3 ) ^{3} ( - 6 x - 61 )}{( 3 x - 2 ) ^{6}}

\int_{a}^{b} arctan (x) d x

4 y^{^{'}} - (\frac{2}{x}) y = (- \frac{3}{2}) x y^{\frac{5}{2}}

x \to 0 lim (\frac{sin ( x )}{7 x})

\int \frac{5 x ^{4} + 7 x ^{2} + x + 2}{x ( x ^{2} + 1 ) ^{2}} d x

\int \frac{1}{x ln ( x ^{3} )} d x

What is the derivative of ((2x+3^4)/((3x-2)^5)) ?
The derivative of ((2x+3^4)/((3x-2)^5)) is ((2x+3)^3(-6x-61))/((3x-2)^6)
What is the first derivative of ((2x+3^4)/((3x-2)^5)) ?
The first derivative of ((2x+3^4)/((3x-2)^5)) is ((2x+3)^3(-6x-61))/((3x-2)^6)