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

The derivative of 5/((4x^{-2)}) is 160x

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

The first derivative of 5/((4x^{-2)}) is 160x

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

160 x

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

2 \cdot 4 x \frac{d}{d x} (4 x)

= 2 \cdot 4 x \frac{d}{d x} (4 x)

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

= 5 \cdot 2 \cdot 4 x \cdot 4

Simplify

= 160 x

\frac{x ^{2}}{1 + x}

\int e^{\frac{- t ^{2}}{2}} d t

x \to + (- 2) - lim (\frac{1}{x ^{2} - 4})

\frac{d}{d x} (cos (wt))

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

What is the derivative of 5/((4x^{-2)}) ?
The derivative of 5/((4x^{-2)}) is 160x
What is the first derivative of 5/((4x^{-2)}) ?
The first derivative of 5/((4x^{-2)}) is 160x