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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

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