SOLUTION: differentiate the following function: (a)f(x)=(x^2+1/x^3 )(x^3-x^2+1) (b)f(x)= e^((x^3+2x))

Algebra ->  Equations -> SOLUTION: differentiate the following function: (a)f(x)=(x^2+1/x^3 )(x^3-x^2+1) (b)f(x)= e^((x^3+2x))       Log On


   

Question 1003759: differentiate the following function:
(a)f(x)=(x^2+1/x^3 )(x^3-x^2+1)
(b)f(x)= e^((x^3+2x))
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
(a)  f%28x%29=%28x%5E2%2B1%2Fx%5E3+%29%28x%5E3-x%5E2%2B1%29

Write 1%2Fx%5E3 as x%5E%28-3%29

f%28x%29=%28x%5E2%2Bx%5E%28-3%29+%29%28x%5E3-x%5E2%2B1%29

Multiply it out first:

f%28x%29=%28x%5E2%2Bx%5E%28-3%29+%29%28x%5E3-x%5E2%2B1%29

f%28x%29=x%5E5-x%5E4%2Bx%5E2%2Bx%5E0-x%5E%28-1%29%2Bx%5E%28-3%29

f%28x%29=x%5E5-x%5E4%2Bx%5E2%2B1-x%5E%28-1%29%2Bx%5E%28-3%29

Take the derivative of each term:

%22f%27%28x%29%22=5x%5E4-4x%5E3%2B2x%2Bx%5E%28-2%29-3x%5E%28-4%29

Changing negative exponents to
positive exponents in denominators.

%22f%27%28x%29%22=+5x%5E4-4x%5E3%2B2x%2B1%2Fx%5E2-3%2Fx%5E4

------------------------------------
(b)  matrix%282%2C1%2C%22%22%2Cf%28x%29=+e%5E%28x%5E3%2B2x%29%29

Rule:  copy it over and multiply by the derivative of the exponent:

matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22=+e%5E%28x%5E3%2B2x%29%2A%283x%5E2%2B2%29%29

Edwin