What is the derivative of y=(8x^3+5)^{3/2} ?

The derivative of y=(8x^3+5)^{3/2} is 36x^2(8x^3+5)^{1/2}

What is the first derivative of y=(8x^3+5)^{3/2} ?

The first derivative of y=(8x^3+5)^{3/2} is 36x^2(8x^3+5)^{1/2}

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derivative of

y = (8 x^{3} + 5)^{\frac{3}{2}}

36 x^{2} (8 x^{3} + 5)^{\frac{1}{2}}

Solution steps

\frac{d}{d x} ((8 x^{3} + 5)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 8 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (8 x^{3} + 5)

= \frac{3 ( 8 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (8 x^{3} + 5)

\frac{d}{d x} (8 x^{3} + 5) = 24 x^{2}

= \frac{3 ( 8 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \cdot 24 x^{2}

Simplify

\frac{3 ( 8 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \cdot 24 x^{2} : 36 x^{2} (8 x^{3} + 5)^{\frac{1}{2}}

= 36 x^{2} (8 x^{3} + 5)^{\frac{1}{2}}

y = e^{x}, y = e^{- 2 x}, x = ln (6)

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

\frac{480 x}{( x ^{2} + 5 ) ^{3}}

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

f (x) = (x^{2} - 8)^{2}

What is the derivative of y=(8x^3+5)^{3/2} ?
The derivative of y=(8x^3+5)^{3/2} is 36x^2(8x^3+5)^{1/2}
What is the first derivative of y=(8x^3+5)^{3/2} ?
The first derivative of y=(8x^3+5)^{3/2} is 36x^2(8x^3+5)^{1/2}