What is the derivative of sin 5xsin5x?
1 Answer
Explanation:
Use the chain rule.
The chain rule states that, in the case of a sine function,
d/dx[sinu]=cosu*(du)/dxddx[sinu]=cosu⋅dudx
More generally, the chain rule says to identify an inside function and an outside function. Here, the outside function is
The chain rule then says to differentiate the outside function, and the derivative of
The final step of this is to multiply the function by the derivative of the inside function, and the derivative of
Thus, the derivative of the whole function is
Using the rule given at the top:
d/dx[sin5x]=cos5x*d/dx[5x]=cos5x*5=5cos5xddx[sin5x]=cos5x⋅ddx[5x]=cos5x⋅5=5cos5x
