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

The derivative of x^2(x^2+5^2) is 6x^5+40x^3+50x

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

The first derivative of x^2(x^2+5^2) is 6x^5+40x^3+50x

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

6 x^{5} + 40 x^{3} + 50 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x^{2} + 5)^{2} + 4 x (x^{2} + 5) x^{2} : 6 x^{5} + 40 x^{3} + 50 x

= 6 x^{5} + 40 x^{3} + 50 x

What is the derivative of x^2(x^2+5^2) ?
The derivative of x^2(x^2+5^2) is 6x^5+40x^3+50x
What is the first derivative of x^2(x^2+5^2) ?
The first derivative of x^2(x^2+5^2) is 6x^5+40x^3+50x