Question

How to find the derivative of g(w) = (eπ)^(w^2)?

a) 2w(eπ)^(w^2)
b) 2we^(w^2)
c) 2wπ(eπ)^(w^2)
d) 2wπe^(w^2)

Answer 1

The derivative of g(w) = (eπ)^(w^2) is found using the chain rule, resulting in 2w(eπ)^(w^2), which is option (a).

Step-by-step explanation:

To find the derivative of g(w) = (eπ)^(w^2), we need to use the chain rule. The chain rule in calculus is a formula for computing the derivative of the composition of two or more functions. In this case, we have an exponential function where the base is a constant (eπ) and the exponent is a function of w (w^2).

The derivative of e^x with respect to x is e^x, but since our exponent is not simply w but w^2, we need to multiply by the derivative of the exponent. So, we differentiate w^2 with respect to w to get 2w. Putting it all together, the derivative of g(w) is 2w(eπ)^(w^2), which matches option (a). Therefore, the correct answer is option (a).