Question

Differentiate the following functions y=4x^3-2x^2+5x^-3.7-6

Answer 1

To differentiate we know that the rule is KX^n= (K*n)X^(n-1) where "K" is some constant , "X" is some variable and "n" is your exponent. so just apply this rule to your function. the first part is 4x^3. to differentiate you follow the rule. (4*3)x^(3-1). you get 12x^2. keep following this rule to the very end even with that -3.7 exponent. dont let the negative or the decimal point trip you up. and take care to change any positive to negative and vice versa should you need to. any how you should get y'=12x²-4x-18.5x^(-4.7)

remember that the 6 is no longer there because the derivative of a constant is zero :)

Answer 2

I don't think you copied it correctly, but I'll assume that you did.

y = 4x³ - 2x² + 5('x' to the -3.7 power) - 6

"y-prime" (the first derivative) =  12x² - 4x - 18.5('x' to the -4.7 power)