What is the derivative of x(x^2+4)^5 ?

The derivative of x(x^2+4)^5 is (x^2+4)^5+10x^2(x^2+4)^4

What is the first derivative of x(x^2+4)^5 ?

The first derivative of x(x^2+4)^5 is (x^2+4)^5+10x^2(x^2+4)^4

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derivative of

x (x^{2} + 4)^{5}

(x^{2} + 4)^{5} + 10 x^{2} (x^{2} + 4)^{4}

Solution steps

\frac{d}{d x} (x (x^{2} + 4)^{5})

Apply the Product Rule:

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

f = x, g = (x^{2} + 4)^{5}

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

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

\frac{d}{d x} ((x^{2} + 4)^{5}) = 10 x (x^{2} + 4)^{4}

= 1 \cdot (x^{2} + 4)^{5} + 10 x (x^{2} + 4)^{4} x

Simplify

1 \cdot (x^{2} + 4)^{5} + 10 x (x^{2} + 4)^{4} x : (x^{2} + 4)^{5} + 10 x^{2} (x^{2} + 4)^{4}

= (x^{2} + 4)^{5} + 10 x^{2} (x^{2} + 4)^{4}

f (x) = 5 x + 2 x^{2} + 7 e^{x}

y = - x^{2} + 1, y = 0

\int_{0}^{π} \frac{1}{π - x} d x

x \to - \frac{5}{2} lim (- x + 2)

\frac{d}{d x} (cos (x) - 1)

What is the derivative of x(x^2+4)^5 ?
The derivative of x(x^2+4)^5 is (x^2+4)^5+10x^2(x^2+4)^4
What is the first derivative of x(x^2+4)^5 ?
The first derivative of x(x^2+4)^5 is (x^2+4)^5+10x^2(x^2+4)^4