What is the derivative of (2x)/((1-4x)^5) ?

The derivative of (2x)/((1-4x)^5) is (2(1+16x))/((1-4x)^6)

What is the first derivative of (2x)/((1-4x)^5) ?

The first derivative of (2x)/((1-4x)^5) is (2(1+16x))/((1-4x)^6)

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derivative of

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

\frac{2 ( 1 + 16 x )}{( 1 - 4 x ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{2 x}{( 1 - 4 x ) ^{5}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((1 - 4 x)^{5}) = - 20 (1 - 4 x)^{4}

= 2 \cdot \frac{1 \cdot ( 1 - 4 x ) ^{5} - ( - 20 ( 1 - 4 x ) ^{4} ) x}{( ( 1 - 4 x ) ^{5} ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( 1 - 4 x ) ^{5} - ( - 20 ( 1 - 4 x ) ^{4} ) x}{( ( 1 - 4 x ) ^{5} ) ^{2}} : \frac{2 ( 1 + 16 x )}{( 1 - 4 x ) ^{6}}

= \frac{2 ( 1 + 16 x )}{( 1 - 4 x ) ^{6}}

What is the derivative of (2x)/((1-4x)^5) ?
The derivative of (2x)/((1-4x)^5) is (2(1+16x))/((1-4x)^6)
What is the first derivative of (2x)/((1-4x)^5) ?
The first derivative of (2x)/((1-4x)^5) is (2(1+16x))/((1-4x)^6)