Solve fsin^-1(1/sqrt{2})

$$f \sin ^ { - 1 } ( \frac { 1 } { \sqrt { 2 } } )$$

Evaluate

$$\frac{250000000000000000f}{3085257053742471}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$f 0.012341028214969884 ^ {-1}$$

Calculate 0.012341028214969884 to the power of -1 and get \frac{250000000000000000}{3085257053742471}.

$$f\times \frac{250000000000000000}{3085257053742471}$$

Differentiate w.r.t. f

$$\frac{250000000000000000}{3085257053742471} = 81\frac{94178646859849}{3085257053742471} = 81.03052538093888$$

Steps Using Definition of a Derivative

Evaluate trigonometric functions in the problem

$$f 0.012341028214969884 ^ {-1}$$

Calculate 0.012341028214969884 to the power of -1 and get \frac{250000000000000000}{3085257053742471}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{250000000000000000}{3085257053742471})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{250000000000000000}{3085257053742471}f^{1-1}$$

Subtract 1 from 1.

$$\frac{250000000000000000}{3085257053742471}f^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{250000000000000000}{3085257053742471}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{250000000000000000}{3085257053742471}$$