Differential Calculus Problem Example 1

Description:

Problem

Calculate the derivatives of following functions −

f(x) = e^x sin x ln x

Solution

To Calculate d/dx(f(x)),

Applying product law, d(u x v)/dx = u dv/dx + v du/dx, (consdering u = (sin x ln x), and v = e^x)

d/dx(e^x sin x ln x) = (sin x ln x)d(e^x)/dx + (e^x) d(sin x ln x)/dx

Again, applying product law in the second bracket, (consdering u = ln x, and v = sin x)

(sin x ln x) d(e^x)/dx + (e^x) [(ln x) d(sin x)/dx + (sin x) d(ln x)/dx]

d/dx(f((x)) = e^x sin x ln x + e^x ln x cos x + e^x sin x/x