Find the Derivative - d/dx (sin(2x))/(cos(x))

Problem

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

Solution

1. Apply the double-angle identity for sine, which states sin(2*x)=2*sin(x)*cos(x) to rewrite the numerator.

sin(2*x)/cos(x)=(2*sin(x)*cos(x))/cos(x)

2. Simplify the expression by canceling the common factor cos(x) from the numerator and the denominator, assuming cos(x)≠0

(2*sin(x)*cos(x))/cos(x)=2*sin(x)

3. Differentiate the simplified expression 2*sin(x) with respect to x using the constant multiple rule and the derivative of the sine function.

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

Final Answer

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

Want more problems? Check here!