What is the derivative of sin(ax)? Calculus Differentiating Trigonometric Functions Differentiating sin(x) from First Principles 1 Answer Bill K. Jul 30, 2015 acos(ax) Explanation: We know d/dx(sin(x))=cos(x) and d/dx(f(g(x))=f'(g(x))*g'(x) (the Chain Rule). Use these two rules now, with f(x)=sin(x) and g(x)=a x (where a is a constant). Answer link Related questions How do you differentiate f(x)=sin(x) from first principles? What is the derivative of y=3sin(x) - sin(3x)? How do you find dy/dx if x + tan(xy) = 0? How do you find the derivative of the function y=cos((1-e^(2x))/(1+e^(2x)))? How do you differentiate f(x)=2secx+(2e^x)(tanx)? How do you find the derivate for y = pisinx - 4cosx? How do you find the derivative of f(t) = t^2sin t? What is the derivative of sin^2(lnx)? How do you compute the 200th derivative of f(x)=sin(2x)? How do you find the derivative of sin(x^2+1)? See all questions in Differentiating sin(x) from First Principles Impact of this question 64525 views around the world You can reuse this answer Creative Commons License