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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

\frac{( - 1 ) ( 3 - x ) ^{4} - ( - 4 ( 3 - x ) ^{3} ) ( 2 - x )}{( ( 3 - x ) ^{4} ) ^{2}} : \frac{- 3 x + 5}{( 3 - x ) ^{5}}

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

\frac{d}{d x} (5 x e^{- x})

\int_{- 4}^{- 1} - \frac{4}{x ^{3}} d x

y^{^{'}} + 3 y = e^{t}

t an g e n t f (x) = 110 x - 16 x^{2}, at

p a r i t y y = ln e^{1 + x^{2}} + 3 x^{4} + cot^{2} (π x)

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