SOLUTION: Find the derivatives of the following functions: (a) f(x) =√x cos x (b) g(x) = (x^3 + 1) / (sin x) (c) h(x) = e^x sin(2x) (d) k(x) = (x^2) / (log x)
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Question 1032383
:
Find the derivatives of the following functions:
(a) f(x) =√x cos 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
Alan3354(69443)
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Find the derivatives of the following functions:
(a) f(x) = sqrt(x)*cos(x)
f'(x) = d/dx(sqrt(x))*cos(x) = sqrt(x)*d/dx(cos(x))
= (1/2)/sqrt(x)*cos(x) - sqrt(x)*sin(x)
= 2sqrt(x)*cos(x)/x - sqrt(x)*sin(x)
====================
(b) g(x) = (x^3 + 1) / (sin x)
g(x) = (x^3+1)*csc(x)
===================
(c) h(x) = e^x sin(2x)
Too easy.
===============
(d) k(x) = (x^2) / (log x) --- assuming natural logs
k(x) = x^2*(log(x))^-1
k'(x) = 2x*(log(x))^-1 + x^2*(-1)*(log(x))^-2*(1/x)
= 2x/ln(x) - x/(ln(x))^2
