What is the derivative of y= 4/((sqrt(2x))^3) ?

The derivative of y= 4/((sqrt(2x))^3) is -(3sqrt(x^2))/(sqrt(2)x^{7/2)}

What is the first derivative of y= 4/((sqrt(2x))^3) ?

The first derivative of y= 4/((sqrt(2x))^3) is -(3sqrt(x^2))/(sqrt(2)x^{7/2)}

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derivative of

y = \frac{4}{( 2 x ) ^{3}}

- \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{4}{( 2 x ) ^{3}})

Simplify

\frac{4}{( 2 x ) ^{3}} : \frac{2}{x ^{3}}

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

Apply the chain rule:

\frac{1}{2 \frac{2}{x ^{3}}} \frac{d}{d x} (\frac{2}{x ^{3}})

= \frac{1}{2 \frac{2}{x ^{3}}} \frac{d}{d x} (\frac{2}{x ^{3}})

\frac{d}{d x} (\frac{2}{x ^{3}}) = - \frac{6}{x ^{4}}

= \frac{1}{2 \frac{2}{x ^{3}}} (- \frac{6}{x ^{4}})

Simplify

\frac{1}{2 \frac{2}{x ^{3}}} (- \frac{6}{x ^{4}}) : - \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}

= - \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}

\int (- 7 - 7 tan^{2} (θ)) d θ

\frac{d P}{d x} = 0.05 P (1 - \frac{P}{2000})

\frac{\partial}{\partial x} (5 x + 8 y + 10 z)

f^{^{'}} (x) = \frac{x ^{2}}{( 9 + 4 x )}

y^{3} d x - x y^{2} d y + x^{3} d x = 0

What is the derivative of y= 4/((sqrt(2x))^3) ?
The derivative of y= 4/((sqrt(2x))^3) is -(3sqrt(x^2))/(sqrt(2)x^{7/2)}
What is the first derivative of y= 4/((sqrt(2x))^3) ?
The first derivative of y= 4/((sqrt(2x))^3) is -(3sqrt(x^2))/(sqrt(2)x^{7/2)}