Find the Derivative - d/d@VAR f(x)=1+7sin(x)-tan(x)

Problem

d()/d(x)*(1+7*sin(x)−tan(x))

Solution

1. Apply the sum and difference rule for derivatives, which allows for the differentiation of each term individually.

d()/d(x)*(1)+d()/d(x)*(7*sin(x))−d()/d(x)*(tan(x))

2. Differentiate the constant term using the rule that the derivative of any constant is zero.

d(1)/d(x)=0

3. Apply the constant multiple rule to the second term, moving the coefficient outside the derivative.

7⋅d(sin(x))/d(x)

4. Differentiate the trigonometric functions using the standard derivative rules where the derivative of sin(x) is cos(x) and the derivative of tan(x) is sec2(x)

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

d(tan(x))/d(x)=sec2(x)

5. Combine the results to find the final expression for the derivative.

0+7*cos(x)−sec2(x)

Final Answer

d()/d(x)*(1+7*sin(x)−tan(x))=7*cos(x)−sec2(x)

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