What is the derivative of f(x)=8(2x-3)^3 ?

The derivative of f(x)=8(2x-3)^3 is 48(2x-3)^2

What is the first derivative of f(x)=8(2x-3)^3 ?

The first derivative of f(x)=8(2x-3)^3 is 48(2x-3)^2

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derivative of

f (x) = 8 (2 x - 3)^{3}

48 (2 x - 3)^{2}

Solution steps

\frac{d}{d x} (8 (2 x - 3)^{3})

Take the constant out:

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

= 8 \frac{d}{d x} ((2 x - 3)^{3})

Apply the chain rule:

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

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

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

= 8 \cdot 3 (2 x - 3)^{2} \cdot 2

Simplify

= 48 (2 x - 3)^{2}

(- 3, 7), (6, - 8)

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What is the derivative of f(x)=8(2x-3)^3 ?
The derivative of f(x)=8(2x-3)^3 is 48(2x-3)^2
What is the first derivative of f(x)=8(2x-3)^3 ?
The first derivative of f(x)=8(2x-3)^3 is 48(2x-3)^2