What is (\partial)/(\partial x)(A^3(x/d)^2) ?

The answer to (\partial)/(\partial x)(A^3(x/d)^2) is (2A^3x)/(d^2)

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(\partial)/(\partial x)(A^3(x/d)^2)

\frac{\partial}{\partial x} (A^{3} (\frac{x}{d})^{2})

\frac{2 A ^{3} x}{d ^{2}}

Solution steps

\frac{\partial}{\partial x} (A^{3} (\frac{x}{d})^{2})

Treat

A, d

as a constant

Take the constant out:

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

= A^{3} \frac{\partial}{\partial x} ((\frac{x}{d})^{2})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{x}{d}) = \frac{1}{d}

= A^{3} \cdot 2 \cdot \frac{x}{d} \cdot \frac{1}{d}

Simplify

A^{3} \cdot 2 \cdot \frac{x}{d} \cdot \frac{1}{d} : \frac{2 A ^{3} x}{d ^{2}}

= \frac{2 A ^{3} x}{d ^{2}}

\frac{d}{d x} (\frac{x ^{3}}{y})

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

\frac{d}{d x} (\frac{6}{5} e^{- 20 x})

ln (\frac{x}{2}), x = 2

x \to - 1 lim (x^{5} - 1)

What is (\partial)/(\partial x)(A^3(x/d)^2) ?
The answer to (\partial)/(\partial x)(A^3(x/d)^2) is (2A^3x)/(d^2)