Find the Derivative - d/dx sin(x) natural log of x

Problem

d()/d(x)*sin(x)*ln(x)

Solution

1. Identify the expression as a product of two functions, u=sin(x) and v=ln(x) which requires the product rule.

2. Apply the product rule formula, which states that (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the individual components: d(sin(x))/d(x)=cos(x) and d(ln(x))/d(x)=1/x

4. Substitute these derivatives back into the product rule formula.

5. Simplify the resulting expression into its final form.

Final Answer

(d(sin(x))*ln(x))/d(x)=sin(x)/x+cos(x)*ln(x)

Want more problems? Check here!