What is the derivative of (2x^3+3)^6 ?

The derivative of (2x^3+3)^6 is 36x^2(2x^3+3)^5

What is the first derivative of (2x^3+3)^6 ?

The first derivative of (2x^3+3)^6 is 36x^2(2x^3+3)^5

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derivative of

(2 x^{3} + 3)^{6}

36 x^{2} (2 x^{3} + 3)^{5}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

= 36 x^{2} (2 x^{3} + 3)^{5}

(2 x - 3)^{6}

x \to 0 + lim (e^{c o t (x)})

\frac{d y}{d x} = \frac{y}{x} + \frac{y ^{2}}{x}

x \to 1 lim (2 x^{3})

What is the derivative of (2x^3+3)^6 ?
The derivative of (2x^3+3)^6 is 36x^2(2x^3+3)^5
What is the first derivative of (2x^3+3)^6 ?
The first derivative of (2x^3+3)^6 is 36x^2(2x^3+3)^5