Exam 1: Derivative as a function / Differentiation

differentiate y = x^ -2/5

(-2/5)x ^ -7/5

23) differentiate z= (A / y^10) + Bcos y

-10A / y^11 - B sin y

Differentiate f(x)= 186.5

0

differentiate y= 4*pi^2

0

21) differentiate v= t^2 - [ (1)/ 4^(sqrt t^3)]

2t + [ (3)/ (4t (4^ sqrt t^3)]

Differentiate f(x) = x^3 - 4x +6

3x^2 -4

differentiate V(r)= 4/3*pi *r^3

4*pi*r^2

Differentiate f(x)= 5x -1

5

differentiate F(x)= (1/2x)^5

5/32*x^4

23) Find the derivative of the function using the definition of derivative. G(t)= 4t / (t+1)

G ' (t) = 4 / (t+1)^2

27) Find an equation of the tangent line to the curve at the given point. y= x + (sqrt x), (1,2)

y = 1/2x + 1/2

25) Find equation of tangent line and normal line to the curve at the given point. y= 6cosx, (pi/3, 3)

y= -3*(sqrt 3)*x + 3 + [pi*(sqrt 3)]. y= [x / (3 sqrt(3)) + 3 - (pi/(9 sqrt(3))

differentiate y= (x^2+4x+3)/ (sqrt x)

[3/2(sqrt x) + (2/ sqrt x) - 3] / [2x(sqrt x)]

Differentiate f(x)= x- 3sinx

f ' (x)= 1 - 3cosx

19) Find the derivative of the function using the definition of derivative. f(x)= x^3-3x+5

f ' (x)= 3x^2 -3

17) find the derivative of the function using the definition of derivative. f(x)= 1/2x-1/3

f '(x)= 1/2

Find the first and second derivatives of the function. f(x) = x^4 -3x^3 + 16x

f'(x)= 4x^3 -9x^2 + 16, f ''(x)= 12x^2 - 18x

21) Find the derivative of the function using the definition of derivative. g(x)= (sqrt 1+2x)

g '(x)= 1 / [sqrt 1+2x]

Find the first and second derivatives of the function. g(t)= 2 cos t - 3 sin t

g'(t) = -2sin t - 3 cost, g " (t)= -2 cos t + 3 sin t

differentiate f(x) = 1/4 (t^4 +8)

t^3