If g(x) = tan (5x2), then g ′(x) = ?
I've worked this problem out like four times already and I keep getting a complete different answer..So I think I'm doing it wrong.
These are the answers I have gotten while doing this problem.
g'(x)= cosx^2 5tan
g'(x)= 2cosxtan^2
To find the derivative of g(x) = tan(5x^2), you can apply the chain rule. The chain rule states that if you have a composition of functions, the derivative is the derivative of the outer function multiplied by the derivative of the inner function.
In this case, the outer function is tan(x) and the inner function is 5x^2. Let's compute the derivative step by step:
1. Start by finding the derivative of the outer function. The derivative of tan(x) is sec^2(x). So far, we have: g'(x) = sec^2(5x^2).
2. Next, find the derivative of the inner function. The derivative of 5x^2 with respect to x is 10x. Now, we have: g'(x) = sec^2(5x^2) * 10x.
So, the answer for g'(x) is g'(x) = 10x * sec^2(5x^2). This is the correct derivative of g(x) = tan(5x^2).