f y = e x2 , dydx is calculated as(a)2xe2x(b) 2xe(c)2xe2x(d) none of these
Question
f y = e x2 , dydx is calculated as(a)2xe2x(b) 2xe(c)2xe2x(d) none of these
Solution
To calculate dy/dx for the function y = e^x^2, we can use the chain rule. The chain rule states that if we have a composite function, such as 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, let's consider g(x) = x^2 and f(u) = e^u. The derivative of f(u) with respect to u is f'(u) = e^u. The derivative of g(x) with respect to x is g'(x) = 2x.
Now, we can apply the chain rule to find dy/dx. Using the formula dy/dx = f'(g(x)) * g'(x), we have:
dy/dx = f'(g(x)) * g'(x) = e^(g(x)) * 2x = e^(x^2) * 2x
Therefore, the correct answer is (c) 2xe^(2x).
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