Find the Derivative - d/dx f(x)=-cos(x)

Problem

d()/d(x)*(−cos(x))

Solution

1. Identify the constant multiple rule for differentiation, which states that d()/d(x)*[c*ƒ(x)]=cd()/d(x)*ƒ(x)

2. Factor out the constant −1 from the derivative operator.

(d(−)*cos(x))/d(x)=−1⋅d(cos(x))/d(x)

3. Apply the derivative rule for the cosine function, which is d(cos(x))/d(x)=−sin(x)

−1⋅(−sin(x))

4. Simplify the expression by multiplying the two negative signs to get a positive result.

sin(x)

Final Answer

(d(−)*cos(x))/d(x)=sin(x)

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