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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{1 \cdot ( 2 - x ) ^{5} - ( - 5 ( 2 - x ) ^{4} ) ( 2 + x )}{( ( 2 - x ) ^{5} ) ^{2}}

Simplify

\frac{1 \cdot ( 2 - x ) ^{5} - ( - 5 ( 2 - x ) ^{4} ) ( 2 + x )}{( ( 2 - x ) ^{5} ) ^{2}} : \frac{4 ( x + 3 )}{( 2 - x ) ^{6}}

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

f (x) = 73 sin (x) + 7 cos (x)

\int_{1}^{5} \frac{M}{e ^{M}} d M

\int \frac{1}{x ( a + b x )} d x

\frac{d y}{d t} + e^{t} y = - 20 e^{t}

x \to 1 lim (\frac{x - 8}{3 x - 4})

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