What is the derivative of (10x^3+7^{3/2}) ?

The derivative of (10x^3+7^{3/2}) is 45x^2(10x^3+7)^{1/2}

What is the first derivative of (10x^3+7^{3/2}) ?

The first derivative of (10x^3+7^{3/2}) is 45x^2(10x^3+7)^{1/2}

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\frac{d}{d x} ((10 x^{3} + 7)^{\frac{3}{2}})

45 x^{2} (10 x^{3} + 7)^{\frac{1}{2}}

Solution steps

\frac{d}{d x} ((10 x^{3} + 7)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 10 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (10 x^{3} + 7)

= \frac{3 ( 10 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (10 x^{3} + 7)

\frac{d}{d x} (10 x^{3} + 7) = 30 x^{2}

= \frac{3 ( 10 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \cdot 30 x^{2}

Simplify

\frac{3 ( 10 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \cdot 30 x^{2} : 45 x^{2} (10 x^{3} + 7)^{\frac{1}{2}}

= 45 x^{2} (10 x^{3} + 7)^{\frac{1}{2}}

\int 20 x^{3} + \frac{1}{x} d x

\frac{2 x}{6 x - 5}

x \to 0 lim (e^{- x^{2}})

\frac{d y}{d x} = \frac{x - 1}{y - 3}

y = \frac{5}{3}, y = \frac{1}{4 - x ^{2}}

What is the derivative of (10x^3+7^{3/2}) ?
The derivative of (10x^3+7^{3/2}) is 45x^2(10x^3+7)^{1/2}
What is the first derivative of (10x^3+7^{3/2}) ?
The first derivative of (10x^3+7^{3/2}) is 45x^2(10x^3+7)^{1/2}