What is the derivative of (2x^3+5^{10}) ?

The derivative of (2x^3+5^{10}) is 60x^2(2x^3+5)^9

What is the first derivative of (2x^3+5^{10}) ?

The first derivative of (2x^3+5^{10}) is 60x^2(2x^3+5)^9

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\frac{d}{d x} ((2 x^{3} + 5)^{10})

60 x^{2} (2 x^{3} + 5)^{9}

Solution steps

\frac{d}{d x} ((2 x^{3} + 5)^{10})

Apply the chain rule:

10 (2 x^{3} + 5)^{9} \frac{d}{d x} (2 x^{3} + 5)

= 10 (2 x^{3} + 5)^{9} \frac{d}{d x} (2 x^{3} + 5)

\frac{d}{d x} (2 x^{3} + 5) = 6 x^{2}

= 10 (2 x^{3} + 5)^{9} \cdot 6 x^{2}

Simplify

= 60 x^{2} (2 x^{3} + 5)^{9}

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What is the derivative of (2x^3+5^{10}) ?
The derivative of (2x^3+5^{10}) is 60x^2(2x^3+5)^9
What is the first derivative of (2x^3+5^{10}) ?
The first derivative of (2x^3+5^{10}) is 60x^2(2x^3+5)^9