What is the derivative of (2+u^2)^5(5-9u^2)^8 ?

The derivative of (2+u^2)^5(5-9u^2)^8 is 10u(2+u^2)^4(5-9u^2)^8-144u(5-9u^2)^7(2+u^2)^5

What is the first derivative of (2+u^2)^5(5-9u^2)^8 ?

The first derivative of (2+u^2)^5(5-9u^2)^8 is 10u(2+u^2)^4(5-9u^2)^8-144u(5-9u^2)^7(2+u^2)^5

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derivative of

(2 + u^{2})^{5} (5 - 9 u^{2})^{8}

10 u (2 + u^{2})^{4} (5 - 9 u^{2})^{8} - 144 u (5 - 9 u^{2})^{7} (2 + u^{2})^{5}

Solution steps

\frac{d}{d u} ((2 + u^{2})^{5} (5 - 9 u^{2})^{8})

Apply the Product Rule:

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

f = (2 + u^{2})^{5}, g = (5 - 9 u^{2})^{8}

= \frac{d}{d u} ((2 + u^{2})^{5}) (5 - 9 u^{2})^{8} + \frac{d}{d u} ((5 - 9 u^{2})^{8}) (2 + u^{2})^{5}

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

\frac{d}{d u} ((5 - 9 u^{2})^{8}) = - 144 u (5 - 9 u^{2})^{7}

= 10 u (2 + u^{2})^{4} (5 - 9 u^{2})^{8} + (- 144 u (5 - 9 u^{2})^{7}) (2 + u^{2})^{5}

Simplify

= 10 u (2 + u^{2})^{4} (5 - 9 u^{2})^{8} - 144 u (5 - 9 u^{2})^{7} (2 + u^{2})^{5}

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What is the derivative of (2+u^2)^5(5-9u^2)^8 ?
The derivative of (2+u^2)^5(5-9u^2)^8 is 10u(2+u^2)^4(5-9u^2)^8-144u(5-9u^2)^7(2+u^2)^5
What is the first derivative of (2+u^2)^5(5-9u^2)^8 ?
The first derivative of (2+u^2)^5(5-9u^2)^8 is 10u(2+u^2)^4(5-9u^2)^8-144u(5-9u^2)^7(2+u^2)^5