What is the derivative of (6x^3+7^{3/2}) ?

The derivative of (6x^3+7^{3/2}) is 27x^2(6x^3+7)^{1/2}

What is the first derivative of (6x^3+7^{3/2}) ?

The first derivative of (6x^3+7^{3/2}) is 27x^2(6x^3+7)^{1/2}

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\frac{d}{d x} ((6 x^{3} + 7)^{\frac{3}{2}})

27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}

Solution steps

\frac{d}{d x} ((6 x^{3} + 7)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6 x^{3} + 7)

= \frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6 x^{3} + 7)

\frac{d}{d x} (6 x^{3} + 7) = 18 x^{2}

= \frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \cdot 18 x^{2}

Simplify

\frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \cdot 18 x^{2} : 27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}

= 27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}

5 cos (3 t)

\int \frac{x + 3 x ^{2}}{y ^{2}} d x

\int \frac{1}{1 - cos ( x )} d x

\frac{\partial}{\partial u} (u + v^{2})

What is the derivative of (6x^3+7^{3/2}) ?
The derivative of (6x^3+7^{3/2}) is 27x^2(6x^3+7)^{1/2}
What is the first derivative of (6x^3+7^{3/2}) ?
The first derivative of (6x^3+7^{3/2}) is 27x^2(6x^3+7)^{1/2}