Find the Derivative - d/dx f(x)=sin(x)tan(x)

Problem

(d(sin(x))*tan(x))/d(x)

Solution

1. Identify the rule needed for the derivative of a product of two functions, u(x)=sin(x) and v(x)=tan(x)

2. Apply the product rule, 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(tan(x))/d(x)=sec2(x)

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

(d(sin(x))*tan(x))/d(x)=sin(x)*sec2(x)+tan(x)*cos(x)

5. Simplify the second term using the identity tan(x)=sin(x)/cos(x)

tan(x)*cos(x)=sin(x)/cos(x)⋅cos(x)=sin(x)

6. Combine the terms to reach the final simplified expression.

sin(x)*sec2(x)+sin(x)

Final Answer

(d(sin(x))*tan(x))/d(x)=sin(x)*sec2(x)+sin(x)

Want more problems? Check here!