What is the derivative of (3x^2+1)(2x+2)^2 ?

The derivative of (3x^2+1)(2x+2)^2 is 48x^3+72x^2+32x+8

What is the first derivative of (3x^2+1)(2x+2)^2 ?

The first derivative of (3x^2+1)(2x+2)^2 is 48x^3+72x^2+32x+8

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derivative of

(3 x^{2} + 1) (2 x + 2)^{2}

48 x^{3} + 72 x^{2} + 32 x + 8

Solution steps

\frac{d}{d x} ((3 x^{2} + 1) (2 x + 2)^{2})

Apply the Product Rule:

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

f = 3 x^{2} + 1, g = (2 x + 2)^{2}

= \frac{d}{d x} (3 x^{2} + 1) (2 x + 2)^{2} + \frac{d}{d x} ((2 x + 2)^{2}) (3 x^{2} + 1)

\frac{d}{d x} (3 x^{2} + 1) = 6 x

\frac{d}{d x} ((2 x + 2)^{2}) = 4 (2 x + 2)

= 6 x (2 x + 2)^{2} + 4 (2 x + 2) (3 x^{2} + 1)

Simplify

6 x (2 x + 2)^{2} + 4 (2 x + 2) (3 x^{2} + 1) : 48 x^{3} + 72 x^{2} + 32 x + 8

= 48 x^{3} + 72 x^{2} + 32 x + 8

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

\frac{\partial}{\partial x} (e^{x} + sin (y))

x \to 0 + lim (ln (sinh (x)))

\frac{d}{d x} (- 2 sin (x) - x)

f (x) = x + sin (x)

What is the derivative of (3x^2+1)(2x+2)^2 ?
The derivative of (3x^2+1)(2x+2)^2 is 48x^3+72x^2+32x+8
What is the first derivative of (3x^2+1)(2x+2)^2 ?
The first derivative of (3x^2+1)(2x+2)^2 is 48x^3+72x^2+32x+8