What is the derivative of ((4x+3)^8)/((x)^4) ?

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

What is the first derivative of ((4x+3)^8)/((x)^4) ?

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

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derivative of

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

\frac{4 ( 4 x + 3 ) ^{7} ( 4 x - 3 )}{x ^{5}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((4 x + 3)^{8}) = 32 (4 x + 3)^{7}

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

= \frac{32 ( 4 x + 3 ) ^{7} x ^{4} - 4 x ^{3} ( 4 x + 3 ) ^{8}}{( x ^{4} ) ^{2}}

Simplify

\frac{32 ( 4 x + 3 ) ^{7} x ^{4} - 4 x ^{3} ( 4 x + 3 ) ^{8}}{( x ^{4} ) ^{2}} : \frac{4 ( 4 x + 3 ) ^{7} ( 4 x - 3 )}{x ^{5}}

= \frac{4 ( 4 x + 3 ) ^{7} ( 4 x - 3 )}{x ^{5}}

x \to 0 lim (\frac{6}{1 + x})

\frac{\partial}{\partial x} (e^{5 x + 3 y})

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

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

\int x cos (y) d y

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