What is the derivative of (x(6x+2)^3) ?

The derivative of (x(6x+2)^3) is (6x+2)^3+18x(6x+2)^2

What is the first derivative of (x(6x+2)^3) ?

The first derivative of (x(6x+2)^3) is (6x+2)^3+18x(6x+2)^2

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

(6 x + 2)^{3} + 18 x (6 x + 2)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((6 x + 2)^{3}) = 18 (6 x + 2)^{2}

= 1 \cdot (6 x + 2)^{3} + 18 (6 x + 2)^{2} x

Simplify

= (6 x + 2)^{3} + 18 x (6 x + 2)^{2}

- π sin (t) cos (t) (u - 1)

- \frac{3 n ^{2} ( n + 1 ) ^{2}}{2}

π (x^{2} + 6 x + 3)^{2}

\frac{( x + 2 )}{2} + (x + 2)

(5 x + 6 y = 20,) (8 x - 6 y = - 46)

What is the derivative of (x(6x+2)^3) ?
The derivative of (x(6x+2)^3) is (6x+2)^3+18x(6x+2)^2
What is the first derivative of (x(6x+2)^3) ?
The first derivative of (x(6x+2)^3) is (6x+2)^3+18x(6x+2)^2