Find the derivative.
g(x)=cos(x^6)
Isn't the answer -6xsin(x^6)
(d(cos(u))dx = -sin(u)(du/dx)
for g(x)=cos(x^6)
(d g(x))/dx = -6(x^5)cos(x^6)
sorry for the mistake
(d g(x)/dx = -6(x^5) SIN (x^6)
To find the derivative of the function g(x) = cos(x^6), you can use the chain rule.
The chain rule states that if you have a composite function, where one function is inside another function, you can find the derivative by multiplying the derivative of the outer function by the derivative of the inner function.
In this case, the outer function is cos(x) and the inner function is x^6.
The derivative of the outer function cos(x) is -sin(x).
To find the derivative of the inner function x^6, you can use the power rule.
The power rule states that if you have a function of the form f(x) = x^n, then the derivative of f(x) with respect to x is given by f'(x) = nx^(n-1).
Applying the power rule to x^6, we get the derivative of x^6 as 6x^(6-1) = 6x^5.
Now, use the chain rule to find the derivative of g(x) = cos(x^6).
g'(x) = -sin(x^6) * 6x^5
So, the derivative of g(x) = cos(x^6) is -6x^5sin(x^6), not -6xsin(x^6) as you mentioned.
Note: It is common to use the notation g'(x) or dy/dx to denote the derivative of a function.