SOLUTION: Find the derivatives of the following functions (a) f(x) = sqrt x cos x ( sqrt is only on x ) (b) g(x) = (x^3 + 1)/sin x (c) h(x) = e^x sin(2x) (d) k(x) = x^2 / log x

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the derivatives of the following functions (a) f(x) = sqrt x cos x ( sqrt is only on x ) (b) g(x) = (x^3 + 1)/sin x (c) h(x) = e^x sin(2x) (d) k(x) = x^2 / log x      Log On


   



Question 1032805: Find the derivatives of the following functions
(a) f(x) = sqrt x cos x ( sqrt is only on x )
(b) g(x) = (x^3 + 1)/sin x
(c) h(x) = e^x sin(2x) (d) k(x) = x^2 / log x

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
. .
apply respective rules:
f(x) = sqrt%28+x%29+cos+%28x%29+ |Apply Multiplication Rule
f' = cos%28x%29%2F2sqrt%28x%29+-+sqrt%28x%29sin%28x%29
g(x) = %28x%5E3+%2B+1%29%2Fsin+%28x%29+ |Apply Division Rule
g' = |Apply Multiplication Rule / chain rule
h' = 2%28e%5Ex%29+cos%282x%29+%2B+%28e%5Ex%29+sin%282x%29 0r %28e%5Ex%29%28sin%282x%29+%2B+2cos%282x%29%29
k(x) = x%5E2+%2F+log+x |Apply Division Rule
k' = +%282xln%28x%29+-+x%5E2%281%2Fx%29%29%2Fln%5E2%28x%29+ or 2x%2Fln%28x%29+-+x%2Fln%5E2%28x%29