a.How do you find the equation of A tangent line to the curve, y=tanx at given points (π/4, 1)?

Question

b.Using product rule twice to prove that f,g, and h are differentiable, then:
(fgh)'=f'gh+fg'h+fgh'

c. Find equation of a tangent line to the curve y=x+cosx at points (O,1)

d.If f(x)= 3x²+5x, find f'(2) and use it to find an equation of the tangent line to the parabola y=3x²-5x at the point (2,2)

Answer 1

i'm not gonna do the questiong for you cos it's YOUR homework...! but here's how you do it!

a.
- find the derivative of y = tan x
- derivative (y') will be m
- equation of tangent y = mx + c
- substitute m, x, and y into the equation (m = y', x = π/4, y = 1)
- rearrange to find c
- then rewrite the equation with m and c!

b. the product rule is
y' = u' * v + v' * u

c. same as for a. but sub in x = 0 and y - 1

d. same as for a. but sub in x = 2 and y =2

Answer 2

Okay, since you posted twice I wil help you with your second question also. All you have to do is consider f to be one function and treat gh as if it were one function; use the product rule to differentiate and then use the product rule again on (gh)`.

Answer 3

a) y' = sec^2(x)
y'(π/4) = sec^2(π/4)
1 = sec^2(π/4)*(π/4) + b
b = 1 - sec^2(π/4)*(π/4)
y = sec^2(π/4)*x + 1 - sec^2(π/4)*(π/4)

b) restate question

c) y' = 1 -sinx
y = (1-sinx)*x+b
1 = b
y = x + b = x+1

d) f'(2) = 6*(2) + 5 = 17
y = 17*x + b
2 = 17*2 + b
b = -32
y = 17*x - 32