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

Problem

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

Solution

1. Identify the rule needed for the expression, which is the product rule for differentiation.

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

3. Assign the functions u=sin(x) and v=tan(x)

4. Differentiate each part individually to find d(sin(x))/d(x)=cos(x) and d(tan(x))/d(x)=sec2(x)

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

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

6. 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)

7. Combine the terms to reach the final simplified form.

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

Final Answer

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

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