Find the derivatives of the following functions f x 16x53

Find the derivatives of the following functions f (x) = 16x^5/\'3 + 50x^1/2 - 5x^-9 g(x) = 36 Squarerootx^2 - 16 f(t) = e^(t^5 + t - 8) - 49 In t (This is NOT a product.)

Solution

b) g(x) = 36 sqrt ( x^2 - 16 )

derivative = 36 d / dx sqrt ( x^2 - 16 )

let x^2 - 16 = y

36 d/dy sqrt ( y) * d/dx ( x^2 - 16 )

d/dy sqrt y = 1 / 2 sqrt y

d/dx (x^2 - 16) = 2x

therefore, derivative = 36 ( 1/ 2 sqrt y ) * 2x

= 36 ( 1* 2x/ {2 sqrt ( x^2 - 16)} )

= 36 x / sqrt ( x^2 - 16 )