find the derivative of the function f(x)=(x ^{3}+x ^{2}-x-1)(x ^{2}+3)

Question

find  the  derivative of the function f(x)=(x ^{3}+x ^{2}-x-1)(x ^{2}+3)

anonymous · Answer

$$f(x) = x^3+x^{(2-x-1)}(x^2+3)$$

anonymous · Answer

please confirm the above equation!

anonymous · Answer

attachment

anonymous · Answer

find  the  derivative of the function f(x)=(x ^{3}+x ^{2}$$find the derivative of the function f(x)=(x ^{3}+x ^{2}-x-1)(x ^{2}+3) $$

anonymous · Answer

$$f(x)=(x ^{3}+x ^{2}-x-1)(x ^{2}+3)$$

anonymous · Answer

yes

anonymous · Answer

ok this is two functions multiplied by each other, therefore we need to apply the product rule

anonymous · Answer

which means we differentiate one function and we leave the other one as it is, and we differentiate the other function and leave the other one as it is...

anonymous · Answer

now step one

anonymous · Answer

apply the product rule
$$(f.g) = f \prime . g +f . g \prime$$

anonymous · Answer

$$=(3x ^{2}+2x -1)(x ^{2}+3) + (x^3+x^2-x-1)(2x)$$

anonymous · Answer

do you need to simplify this expression

anonymous · Answer

this is your final answer but you can simplify it if you want

anonymous · Answer

there is another way to solve this problem is to multiply the two functions then differentiate it

anonymous · Answer

yes

anonymous · Answer

when you expand this function you see that:

anonymous · Answer

$$f(x) = x^5 + 2x^3+x^4+2x^2-3x-3$$

anonymous · Answer

$$f \prime (x) = 5x^4+6x^2+4x^3+4x-3$$

anonymous · Answer

i think this way is easier for you to see and visualise

anonymous · Answer

you know how to multiply two polynomials right?!