hawkblader said:1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4 sinx))) (e^(x^4 sinx)) (4x^3 cosx+4*3x^2 sinx)
Product rule.hawkblader said:Could you please tell me how you got the blue part?
I put it in and it's still wrong :(
hawkblader said:1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4 sinx))) (e^(x^4 sinx)) (4x^3 cosx)
The chain rule is a formula used to find the derivative of a composite function, which is a function that is composed of two or more functions. It states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.
To apply the chain rule, you need to first identify the outer function, the inner function, and their respective derivatives. Then, you can use the formula: f'(g(h(x))) = f'(g(h(x))) * g'(h(x)) * h'(x). Simply substitute the derivatives of each function into the formula and solve for f'(g(h(x))).
Sure! Let's say we have the function f(x) = sin(2x^2). The outer function is sin(x), the inner function is 2x^2, and their respective derivatives are cos(x) and 4x. Using the chain rule, we can find the derivative as follows: f'(x) = cos(2x^2) * 4x = 4xcos(2x^2).
Yes, there are a few special cases when using the chain rule. One is when the outer function is a constant, in which case its derivative is 0. Another is when the inner function is a constant, in which case its derivative is also 0. In these cases, the chain rule simplifies to f'(g(h(x))) = f'(g(x)) * g'(x).
One tip is to always check your work by applying the chain rule in reverse, starting with the derivative and working backwards to the original function. Another tip is to practice simplifying the function before applying the chain rule, which can make the process easier and less prone to errors.