What is the derivative of x(x^2+7)^4 ?

The derivative of x(x^2+7)^4 is (x^2+7)^4+8x^2(x^2+7)^3

What is the first derivative of x(x^2+7)^4 ?

The first derivative of x(x^2+7)^4 is (x^2+7)^4+8x^2(x^2+7)^3

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derivative of

x (x^{2} + 7)^{4}

(x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

Solution steps

\frac{d}{d x} (x (x^{2} + 7)^{4})

Apply the Product Rule:

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

f = x, g = (x^{2} + 7)^{4}

= \frac{d x}{d x} (x^{2} + 7)^{4} + \frac{d}{d x} ((x^{2} + 7)^{4}) x

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

\frac{d}{d x} ((x^{2} + 7)^{4}) = 8 x (x^{2} + 7)^{3}

= 1 \cdot (x^{2} + 7)^{4} + 8 x (x^{2} + 7)^{3} x

Simplify

1 \cdot (x^{2} + 7)^{4} + 8 x (x^{2} + 7)^{3} x : (x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

= (x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

What is the derivative of x(x^2+7)^4 ?
The derivative of x(x^2+7)^4 is (x^2+7)^4+8x^2(x^2+7)^3
What is the first derivative of x(x^2+7)^4 ?
The first derivative of x(x^2+7)^4 is (x^2+7)^4+8x^2(x^2+7)^3