Question

find (a) the derivative of f(x)s(x) without using the product rule, and (b) f(x)s(x). note that the answer to part (b) is different from the answer to part (a). f(x)=x^4 + 1, s(x)=x^6 (a) the derivative of f(x)s(x) is □.

Explanation:

Step1: First find the product of F(x) and S(x)

$F(x)S(x)=(x^{4}+1)x^{6}=x^{10}+x^{6}$

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = x^{n}$, then $y^\prime=nx^{n - 1}$.
For $y=x^{10}+x^{6}$, the derivative $y^\prime=(x^{10})^\prime+(x^{6})^\prime$.
$(x^{10})^\prime = 10x^{9}$ and $(x^{6})^\prime=6x^{5}$.
So, $y^\prime = 10x^{9}+6x^{5}$

Answer:

$10x^{9}+6x^{5}$