Find dy/dx y=6x-4cos(3x)

Problem

y=6*x−4*cos(3*x)

Solution

1. Identify the structure of the function as a difference of two terms, 6*x and 4*cos(3*x) which allows for the use of the sum/difference rule for differentiation.

2. Differentiate the first term, 6*x using the power rule.

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

3. Apply the chain rule to the second term, 4*cos(3*x) The derivative of cos(u) is −sin(u) and the derivative of the inner function 3*x is 3

(d(4)*cos(3*x))/d(x)=4*(−sin(3*x))⋅3

4. Simplify the derivative of the second term by multiplying the constants.

4*(−sin(3*x))⋅3=−12*sin(3*x)

5. Combine the results of the differentiated terms, noting the subtraction sign in the original expression.

d(y)/d(x)=6−(−12*sin(3*x))

6. Simplify the signs to reach the final derivative.

d(y)/d(x)=6+12*sin(3*x)

Final Answer

d(y)/d(x)=6+12*sin(3*x)

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