What is the derivative of (x^2+3)^4(x+1) ?

The derivative of (x^2+3)^4(x+1) is 8x(x^2+3)^3(x+1)+(x^2+3)^4

What is the first derivative of (x^2+3)^4(x+1) ?

The first derivative of (x^2+3)^4(x+1) is 8x(x^2+3)^3(x+1)+(x^2+3)^4

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derivative of

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

8 x (x^{2} + 3)^{3} (x + 1) + (x^{2} + 3)^{4}

Solution steps

\frac{d}{d x} ((x^{2} + 3)^{4} (x + 1))

Apply the Product Rule:

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

f = (x^{2} + 3)^{4}, g = x + 1

= \frac{d}{d x} ((x^{2} + 3)^{4}) (x + 1) + \frac{d}{d x} (x + 1) (x^{2} + 3)^{4}

\frac{d}{d x} ((x^{2} + 3)^{4}) = 8 x (x^{2} + 3)^{3}

\frac{d}{d x} (x + 1) = 1

= 8 x (x^{2} + 3)^{3} (x + 1) + 1 \cdot (x^{2} + 3)^{4}

Simplify

= 8 x (x^{2} + 3)^{3} (x + 1) + (x^{2} + 3)^{4}

What is the derivative of (x^2+3)^4(x+1) ?
The derivative of (x^2+3)^4(x+1) is 8x(x^2+3)^3(x+1)+(x^2+3)^4
What is the first derivative of (x^2+3)^4(x+1) ?
The first derivative of (x^2+3)^4(x+1) is 8x(x^2+3)^3(x+1)+(x^2+3)^4