Question
d/dx(3sin(-5x)=
Answers
GPT 3.5
To differentiate the function y = 3sin(-5x), we can use the chain rule. The chain rule states that if we have a composite function y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).
In this case, f(u) = 3sin(u) and g(x) = -5x. Taking the derivative of f(u) with respect to u gives f'(u) = 3cos(u). Taking the derivative of g(x) with respect to x gives g'(x) = -5.
Applying the chain rule, we have dy/dx = f'(g(x)) * g'(x) = 3cos(-5x) * (-5) = -15cos(-5x).
Therefore, d/dx(3sin(-5x)) = -15cos(-5x).
In this case, f(u) = 3sin(u) and g(x) = -5x. Taking the derivative of f(u) with respect to u gives f'(u) = 3cos(u). Taking the derivative of g(x) with respect to x gives g'(x) = -5.
Applying the chain rule, we have dy/dx = f'(g(x)) * g'(x) = 3cos(-5x) * (-5) = -15cos(-5x).
Therefore, d/dx(3sin(-5x)) = -15cos(-5x).