What is the derivative of (48/((1-2x)^4)) ?

The derivative of (48/((1-2x)^4)) is (384)/((1-2x)^5)

What is the first derivative of (48/((1-2x)^4)) ?

The first derivative of (48/((1-2x)^4)) is (384)/((1-2x)^5)

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\frac{d}{d x} (\frac{48}{( 1 - 2 x ) ^{4}})

\frac{384}{( 1 - 2 x ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{48}{( 1 - 2 x ) ^{4}})

Take the constant out:

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

= 48 \frac{d}{d x} (\frac{1}{( 1 - 2 x ) ^{4}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 48 \frac{d}{d x} ((1 - 2 x)^{- 4})

Apply the chain rule:

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

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

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

= 48 (- \frac{4}{( 1 - 2 x ) ^{5}} (- 2))

Simplify

48 (- \frac{4}{( 1 - 2 x ) ^{5}} (- 2)) : \frac{384}{( 1 - 2 x ) ^{5}}

= \frac{384}{( 1 - 2 x ) ^{5}}

\frac{d}{d x} (ln (x + 2 + x^{2}))

x y^{2} y^{^{'}} = x^{3} + y^{3}

\int_{0}^{\frac{π}{6}} ln (sec (x)) d x

y = x, y = x^{2}, x = 2

f (t) = t^{3}

What is the derivative of (48/((1-2x)^4)) ?
The derivative of (48/((1-2x)^4)) is (384)/((1-2x)^5)
What is the first derivative of (48/((1-2x)^4)) ?
The first derivative of (48/((1-2x)^4)) is (384)/((1-2x)^5)