Question #05c1d Calculus Differentiating Trigonometric Functions Intuitive Approach to the derivative of y=sin(x) 1 Answer Timber Lin Dec 15, 2017 #=e^sqrt(x)/(2sqrt(x))# Explanation: first, derivative of #e^x# is #e^x# proof derivative of #e^sqrt(x)# is #e^sqrt(x)*d/dx(sqrt(x))# chain rule #=e^sqrt(x)*d/dx(x^(1/2))# #=e^sqrt(x)*(1/2x^(-1/2))# power rule #=e^sqrt(x)/(2sqrt(x))# Answer link Related questions What is the derivative of #-sin(x)#? What is the derivative of #sin(2x)#? How do I find the derivative of #y=sin(2x) - 2sin(x)#? How do you find the second derivative of #y=2sin3x-5sin6x#? How do you compute #d/dx 3sinh(3/x)#? How do you find the derivative #y=xsinx + cosx#? What is the derivative of #sin(x^2y^2)#? What is #f'(-pi/3)# when you are given #f(x)=sin^7(x)#? How do you find the fist and second derivative of #pi*sin(pix)#? If f(x)= 2x sin(x) cos(x), how do you find f'(x)? See all questions in Intuitive Approach to the derivative of y=sin(x) Impact of this question 1476 views around the world You can reuse this answer Creative Commons License