Need help This is Calculus

If y = x^5, then dy/dx = 5x^4

If f(x) = [ g(x) ]^5, then f ' (x) = 5*[ g(x) ]^4 * g ' (x) through the chain rule.

In this case, g(x) = x^3 - cos(x)

This would then mean g ' (x) = 3x^2 + sin(x)

Therefore,

-6 is the correct option from the above given options

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!