What is the derivative of #f(x) = sin^2(x)-cos^2(x)#? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer James Apr 28, 2018 The answer #f'(x)=4*sin(x)*cos(x)# Explanation: show below #f(x)=sin^2(x)-cos^2(x)# #f'(x)=2*sin(x)*cos(x)-[2*cos(x)*-sin(x)]# #f'(x)=2*sin(x)*cos(x)+2*sin(x)*cos(x)# #f'(x)=4*sin(x)*cos(x)# Answer link Related questions What is the derivative of #y=cos(x)# ? What is the derivative of #y=tan(x)# ? How do you find the 108th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x)# from first principle? How do you find the derivative of #y=cos(x^2)# ? How do you find the derivative of #y=e^x cos(x)# ? How do you find the derivative of #y=x^cos(x)#? How do you find the second derivative of #y=cos(x^2)# ? How do you find the 50th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x^2)# ? See all questions in Derivative Rules for y=cos(x) and y=tan(x) Impact of this question 20469 views around the world You can reuse this answer Creative Commons License