Suppose u and v are differentiable functions of x and that

u(1) = 2, u'(1)= 0, v(1)= 5, v'(1)=-1

Find the values of the following derivatives at x =1

a) d/dx (uv)

b) d/dx(u/v)

c) d/dx (v/u)

d) d/dx (7v-2u)

B I personally think..

Step-by-step explanation:

Hi,

Use Differential Formula :

d(u(x) • v(x))/dx = u'(x) • v(x) + u(x) • v'(x)

at x = 1 :

d(u(1) • v(1))/dx = u'(1) • v(1) + u(1) • v'(1)

d(u(1) • v(1))/dx = -5 • 6 + 4  • -2

d(u(1) • v(1))/dx = -30 - 8

d(u(1) • v(1))/dx = -38

Hope this helped :)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240