Find the Derivative - d/dx f(x)=4cos(x)+2sin(x)

Problem

d()/d(x)*(4*cos(x)+2*sin(x))

Solution

1. Apply the sum rule for differentiation, which allows for the derivative of a sum to be taken as the sum of the derivatives.

d()/d(x)*(4*cos(x)+2*sin(x))=(d(4)*cos(x))/d(x)+(d(2)*sin(x))/d(x)

2. Apply the constant multiple rule to move the coefficients outside of the derivative operators.

(d(4)*cos(x))/d(x)+(d(2)*sin(x))/d(x)=4d(cos(x))/d(x)+2d(sin(x))/d(x)

3. Differentiate the trigonometric functions using the standard rules d(cos(x))/d(x)=−sin(x) and d(sin(x))/d(x)=cos(x)

4*(−sin(x))+2*(cos(x))

4. Simplify the expression by multiplying the terms.

−4*sin(x)+2*cos(x)

Final Answer

d()/d(x)*(4*cos(x)+2*sin(x))=−4*sin(x)+2*cos(x)

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