We can solve this by differentiation of a function of a function.
g(u) = (5+u^2)^5(3-9u^2)^8
g(u)=p(u)^5 * q(u)^8
Using the chain rule, we get
=9q(u)^7*(-18u) ... (2)
Now apply the product rule to the original function g(u):
=(p(u)^5*d(q(u))/du + d(p(u))/du * q(u)^8
Substitute (1) and (2) and simplify to get:
or some equivalent expression.
Go to : calc101 com
Click option derivatives
In rectacangle:Take the derivative of
In rectacangle:with respect to:
In rectacangle:and again with respect to
Then click option: DO IT
You will see solution step-by-step
By the way on this site you can practice any kind of derivation.
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