Find the Derivative - d/dx tan(x)cos(x)

Problem

d()/d(x)*tan(x)*cos(x)

Solution

1. Simplify the expression using trigonometric identities before differentiating.

2. Substitute the identity tan(x)=sin(x)/cos(x) into the expression.

tan(x)*cos(x)=sin(x)/cos(x)⋅cos(x)

3. Cancel the common factor of cos(x) in the numerator and denominator.

sin(x)/cos(x)⋅cos(x)=sin(x)

4. Differentiate the simplified expression with respect to x

d(sin(x))/d(x)=cos(x)

Final Answer

d()/d(x)*tan(x)*cos(x)=cos(x)

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