f(x) = e^(sin(x))cos(x)
What question ?
the derivative of f(x) = e^(sin x)cos(x)
f'(x)=e^(sinx)cosx*cosx+e^(sinx)(-sinx)
The function you provided is f(x) = e^(sin(x))cos(x).
To better understand this function, let's break it down step by step:
1. Inside the exponential function e^(sin(x)), sin(x) represents the sine of x. The sine function calculates the ratio of the length of the side opposite the given angle to the length of the hypotenuse in a right triangle.
2. Next, we have the cosine function cos(x). The cosine function calculates the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
3. Finally, we multiply e^(sin(x)) by cos(x).
To evaluate this function at a specific value of x, you need to substitute the value of x into the function and simplify the expression. Here's how you can do it:
Let's say we want to evaluate the function at x = 2.
Step 1: Calculate sin(x). In this case, sin(2) is approximately 0.909, depending on the unit of measurement.
Step 2: Substitute sin(2) into the exponential function: e^(0.909).
Step 3: Calculate e^(0.909). The value of e (Euler's number) is approximately 2.71828. So, e^(0.909) is approximately 2.48096.
Step 4: Calculate cos(x). In this case, cos(2) is approximately -0.41614, depending on the unit of measurement.
Step 5: Multiply the result from step 3 (2.48096) by the result from step 4 (-0.41614). The final result is approximately -1.03103.
Therefore, f(2) ≈ -1.03103.
You can repeat this process for any other value of x to evaluate the function at different points.