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

The derivative of (2x^2-3)^3 is 12x(2x^2-3)^2

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

The first derivative of (2x^2-3)^3 is 12x(2x^2-3)^2

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derivative of

(2 x^{2} - 3)^{3}

12 x (2 x^{2} - 3)^{2}

Solution steps

\frac{d}{d x} ((2 x^{2} - 3)^{3})

Apply the chain rule:

3 (2 x^{2} - 3)^{2} \frac{d}{d x} (2 x^{2} - 3)

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

\frac{d}{d x} (2 x^{2} - 3) = 4 x

= 3 (2 x^{2} - 3)^{2} \cdot 4 x

Simplify

= 12 x (2 x^{2} - 3)^{2}

8 t^{2}

y^{^{'}} + 2 y = 60, y (1) = 80

\frac{d y}{d x} + \frac{3 y}{x} = x^{5} y^{3}

2 x y^{2} + x^{2} y^{^{'}} = y^{2}

y^{^{'}} = y (3 - y), y (0) = 5

What is the derivative of (2x^2-3)^3 ?
The derivative of (2x^2-3)^3 is 12x(2x^2-3)^2
What is the first derivative of (2x^2-3)^3 ?
The first derivative of (2x^2-3)^3 is 12x(2x^2-3)^2