Find the Derivative - d/dx y=7+sin(x)

Problem

d()/d(x)*(7+sin(x))

Solution

1. Identify the expression to be differentiated, which is a sum of a constant and a trigonometric function.

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

d()/d(x)*(7+sin(x))=d(7)/d(x)+d(sin(x))/d(x)

3. Differentiate the constant term. The derivative of any constant with respect to x is 0

d(7)/d(x)=0

4. Differentiate the trigonometric function. The derivative of sin(x) with respect to x is cos(x)

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

5. Combine the results to find the final derivative.

0+cos(x)=cos(x)

Final Answer

d()/d(x)*(7+sin(x))=cos(x)

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