What is the derivative of f(x)=(6x-2)^2*(6x^2+3)^5 ?

The derivative of f(x)=(6x-2)^2*(6x^2+3)^5 is 12(6x-2)(6x^2+3)^5+60x(6x^2+3)^4(6x-2)^2

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

The first derivative of f(x)=(6x-2)^2*(6x^2+3)^5 is 12(6x-2)(6x^2+3)^5+60x(6x^2+3)^4(6x-2)^2

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derivative of

f (x) = (6 x - 2)^{2} \cdot (6 x^{2} + 3)^{5}

12 (6 x - 2) (6 x^{2} + 3)^{5} + 60 x (6 x^{2} + 3)^{4} (6 x - 2)^{2}

Solution steps

\frac{d}{d x} ((6 x - 2)^{2} (6 x^{2} + 3)^{5})

Apply the Product Rule:

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

f = (6 x - 2)^{2}, g = (6 x^{2} + 3)^{5}

= \frac{d}{d x} ((6 x - 2)^{2}) (6 x^{2} + 3)^{5} + \frac{d}{d x} ((6 x^{2} + 3)^{5}) (6 x - 2)^{2}

\frac{d}{d x} ((6 x - 2)^{2}) = 12 (6 x - 2)

\frac{d}{d x} ((6 x^{2} + 3)^{5}) = 60 x (6 x^{2} + 3)^{4}

= 12 (6 x - 2) (6 x^{2} + 3)^{5} + 60 x (6 x^{2} + 3)^{4} (6 x - 2)^{2}

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What is the derivative of f(x)=(6x-2)^2*(6x^2+3)^5 ?
The derivative of f(x)=(6x-2)^2*(6x^2+3)^5 is 12(6x-2)(6x^2+3)^5+60x(6x^2+3)^4(6x-2)^2
What is the first derivative of f(x)=(6x-2)^2*(6x^2+3)^5 ?
The first derivative of f(x)=(6x-2)^2*(6x^2+3)^5 is 12(6x-2)(6x^2+3)^5+60x(6x^2+3)^4(6x-2)^2