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

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

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

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

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derivative of

y = \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{\partial}{\partial x} (sec (y))

\int e^{2 x} cos (\frac{x}{4}) d x

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

\frac{1}{( y ^{2} - 3 y + 2 )} y^{^{'}} = \frac{1}{x}

x \to 3 lim (x - 10)

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