Find the Derivative - d/d@VAR f(x)=2sin(x)+tan(x)

Problem

d()/d(x)*(2*sin(x)+tan(x))

Solution

1. Identify the rule for differentiation, which is the sum rule: the derivative of a sum is the sum of the derivatives.

2. Apply the constant multiple rule to the first term, which states that d()/d(x)*c*ƒ(x)=cd(ƒ(x))/d(x)

3. Differentiate the trigonometric functions using standard derivative rules: d(sin(x))/d(x)=cos(x) and d(tan(x))/d(x)=sec2(x)

4. Combine the results to find the final derivative of the function.

Final Answer

d()/d(x)*(2*sin(x)+tan(x))=2*cos(x)+sec2(x)

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