Question

What is the second derivative of sin(ln(x))² * e^(cos(x)) with respect to x?

a) d²/dx²(sin(ln(x))² * e^(cos(x))) = -sin(ln(x))² * e^(cos(x))
b) d²/dx²(sin(ln(x))² * e^(cos(x))) = sin(ln(x))² * e^(cos(x))
c) d²/dx²(sin(ln(x))² * e^(cos(x))) = cos(x) * sin(ln(x))² * e^(cos(x))
d) d²/dx²(sin(ln(x))² * e^(cos(x))) = -sin(ln(x))² * e^(-cos(x))

Answer 1

The second derivative of sin(ln(x))² * e^(cos(x)) with respect to x is -sin(ln(x))² * e^(cos(x)).

Step-by-step explanation:

To find the second derivative of sin(ln(x))² * e^(cos(x)) with respect to x, we follow the basic rules of differentiation. Let's start by finding the first derivative.

The first derivative of sin(ln(x))² * e^(cos(x)) can be found by using the product rule and the chain rule. The first derivative is: (2sin(ln(x)) * cos(ln(x))) * e^(cos(x)) - sin(ln(x))² * e^(cos(x)) * sin(x).

Now, to find the second derivative, we differentiate the first derivative with respect to x. The second derivative is: -sin(ln(x))² * e^(cos(x)).