We have the product rule in differentiation as follows.
If then .
Now we have .
Thus by the product rule we get
.
Question 11 Find the derivative: f(x) = x2 In 5x 2x (3x In 5x) X+ In...
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
Find the Laplace transform of f (x) = 2 e−3x + cos 2x + 5x.
Find the asymptotes for the following function: x' + 5x f(x) = x2 2-3x - 40
Use the rules to find the derivative f (x) = -3x e^x^5 + 2cos(2x^2 )
9) Find ( 5x+3x+3x dx a) O 5x2 + x3 + x2 + c b) O 5x3 + 2x2 + 3x + c c) O 5x3 + 2.x + 3x + с d) 0 5x + x² + x3 + c 8) Find the most general solution of the differential equation dx C49602 Weight: 1 = 6x2 - 7; given that y = 5, dy = 2, when x = dx o. a) y = PR + 2x + 5...
4. Simplify and state the restrictions. 2x+8 4x+16 a) 3x 6x2–5x+1 b) x2-4 Х x2-x-2 x2-3x 2x2 4 1 c) x2+3x+2 + 1 x2+4x+3 11x d)- x2+3x-28 X-4
Let g(x) =3x + 5 and f(x) = x2 + 2x – 7 . Find f(g(x)).
21) g(x) 2x-2 f(x)=x2 +3x Find (g f-2+x)
Find the derivative of y with respect to x. y= In 1 + 2x X2 OA. -4-3x 2x OB. 4 – 3 x 2x(1 + xx) -4-3/ 2(1+) -4-377 2x(1+x) OD.
1. Write down the definition of the derivative and use it to find f'(x) for f(x)=5x² - 2x