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

The derivative of f(x)=8x(x^2+3)^3 is 8((x^2+3)^3+6x^2(x^2+3)^2)

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

The first derivative of f(x)=8x(x^2+3)^3 is 8((x^2+3)^3+6x^2(x^2+3)^2)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x^{2} + 3)^{3}

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

\frac{d x}{d x} = 1

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

= 8 (1 \cdot (x^{2} + 3)^{3} + 6 x (x^{2} + 3)^{2} x)

Simplify

8 (1 \cdot (x^{2} + 3)^{3} + 6 x (x^{2} + 3)^{2} x) : 8 ((x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2})

= 8 ((x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2})

What is the derivative of f(x)=8x(x^2+3)^3 ?
The derivative of f(x)=8x(x^2+3)^3 is 8((x^2+3)^3+6x^2(x^2+3)^2)
What is the first derivative of f(x)=8x(x^2+3)^3 ?
The first derivative of f(x)=8x(x^2+3)^3 is 8((x^2+3)^3+6x^2(x^2+3)^2)