Find the Derivative - d/dx y=picos(6x+0.71)

Problem

d()/d(x)*π*cos(6*x+0.71)

Solution

1. Identify the constant and the outer function. The term π is a constant coefficient, and the outer function is the cosine function.

2. Apply the constant multiple rule to move the π outside of the derivative operation.

(d(π)*cos(6*x+0.71))/d(x)=πd(cos(6*x+0.71))/d(x)

3. Apply the chain rule, which states that the derivative of cos(u) is −sin(u)⋅d(u)/d(x) Here, u=6*x+0.71

d(cos(6*x+0.71))/d(x)=−sin(6*x+0.71)⋅d(6*x+0.71)/d(x)

4. Differentiate the inner function 6*x+0.71 with respect to x

d(6*x+0.71)/d(x)=6

5. Combine the results by multiplying the constant π the derivative of the outer function, and the derivative of the inner function.

π⋅(−sin(6*x+0.71))⋅6=−6*π*sin(6*x+0.71)

Final Answer

(d(π)*cos(6*x+0.71))/d(x)=−6*π*sin(6*x+0.71)

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