Find the Derivative - d/dx sin(x)cot(x)

Problem

(d(sin(x))*cot(x))/d(x)

Solution

1. Identify the trigonometric identity for the cotangent function, which is cot(x)=cos(x)/sin(x)

2. Substitute this identity into the original expression to simplify the function before differentiating.

sin(x)*cot(x)=sin(x)⋅cos(x)/sin(x)

3. Simplify the expression by canceling the sin(x) terms in the numerator and denominator.

sin(x)⋅cos(x)/sin(x)=cos(x)

4. Differentiate the simplified expression cos(x) with respect to x using the standard derivative rule d(cos(x))/d(x)=−sin(x)

d(cos(x))/d(x)=−sin(x)

Final Answer

(d(sin(x))*cot(x))/d(x)=−sin(x)

Want more problems? Check here!