What is the derivative of (4x^3+5^{3/2}) ?

The derivative of (4x^3+5^{3/2}) is 18x^2(4x^3+5)^{1/2}

What is the first derivative of (4x^3+5^{3/2}) ?

The first derivative of (4x^3+5^{3/2}) is 18x^2(4x^3+5)^{1/2}

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\frac{d}{d x} ((4 x^{3} + 5)^{\frac{3}{2}})

18 x^{2} (4 x^{3} + 5)^{\frac{1}{2}}

Solution steps

\frac{d}{d x} ((4 x^{3} + 5)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 4 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (4 x^{3} + 5)

= \frac{3 ( 4 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (4 x^{3} + 5)

\frac{d}{d x} (4 x^{3} + 5) = 12 x^{2}

= \frac{3 ( 4 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \cdot 12 x^{2}

Simplify

\frac{3 ( 4 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \cdot 12 x^{2} : 18 x^{2} (4 x^{3} + 5)^{\frac{1}{2}}

= 18 x^{2} (4 x^{3} + 5)^{\frac{1}{2}}

\frac{\partial}{\partial x} (\frac{x ^{2} - 1}{y})

x \to 3 lim (2 x^{x^{2}} - 3 x + 2)

\int - 32 x + 12 d x

y^{^{''}} + y = 2 x cos (x)

\frac{\partial}{\partial y} (3 x + 4 y)

What is the derivative of (4x^3+5^{3/2}) ?
The derivative of (4x^3+5^{3/2}) is 18x^2(4x^3+5)^{1/2}
What is the first derivative of (4x^3+5^{3/2}) ?
The first derivative of (4x^3+5^{3/2}) is 18x^2(4x^3+5)^{1/2}