Question

Let f be the function given by f(x)=cosx − cscx. What is the value of f′(1)?

Answer 1

The value of f'(1) is approximately -0.301.

Step-by-step explanation:

To find the value of f′(1), we need to find the derivative of the function f(x)=cosx − cscx and then evaluate it at x=1.

Step 1: Determine the derivative of each term:

f(x)=cosx − cscx

f'(x)=-sinx + cscxcotx

Step 2: Evaluate f′(1):

f′(1)=-sin(1) + csc(1)cot(1)

=-sin(1) + csc(1)(1/tan(1))

=-sin(1) + 1/(sin(1)/cos(1))

=-sin(1) + cos(1)/sin(1)

≈ -0.841 + 0.540

≈ -0.301