Question

find the derivatives of f(x)=x^5(3-6x-9)​

Answer 1

Answer:

Letf * (x) = x ^ 5 * (3 - 6x ^ - 9)

Let u=x^ 5 8 v=3-6x^ -9

So, f(x) = uv

therefore f^ prime (x)=(uv)^ prime

f^ prime (x)=u^ prime v+v^ prime u

Finding u^ prime 8v^ prime

u = x ^ 5

u^ prime =5x^ 5-1

u^ prime =5x^ 4

v = 3 - 6x ^ - 9

v^ prime =0-6(-9)x^ -10

v^ prime =54x^ -10

Now,

f^ prime (x)=(uv)^ prime

=u^ prime v+v^ prime u

=5x^ 4 (3-6x^ -9 )+54x^ -10 (x^ 5 )

=15x^ 4 -30x^ -9+4 +54x^ -10+5

=15x^ 4 -30x^ -5 +54x^ -5

Step-by-step explanation:

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