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

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

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

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

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derivative of

f (x) = (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}

\frac{d}{d x} (\frac{cos ( x )}{2})

- 2 x^{2}

\int 9 x^{2} - 8 x d x

\int \frac{3}{1 + 9 x ^{2}} d x

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