im usually good at math but what the heck is the derivative of f(x)= x+ sin (x+1)?

Question

im usually good at math but what the heck is the derivative of f(x)= x+ sin (x+1)

Answer 1

Look:

f(x)= x+ sin (x+1)

f'(x)= 1+ cos(x+1)

Answer 2

You will have to remember to use the chain rule. It's not *crucially* important here but it will be in later problems (it is likely that they will be in this same problem set).



I'm sure you know that x'=1.



However, sin(x+1) is a composite function of sin and (x+1).



sin(x+1)≠cos(1). (english: do not take the derivative of both parts!)



Chain rule: if y=f(g(x)), and u=g(x) then the derivative of f(g(x)) is f'(u) * g'(x).



In english, it means that you find the derivative of the outermost function (in your case sine) and leave the innermost function (x+1) intact. Then you multiply your shiny new function by the derivative of the innermost function (x+1).



sin(u)' is cos(u), so [x+sin(x+1)]' is



x' + cos(x+1)*(x+1)'

1 + cos(x+1)*1

1 + cos(x+1)



in this case, the innermost function becomes one, so you really didn't have to use chain rule. However, it's better to use it every time so you don't forget it when it's important. Also, if you fail to use chain rule, your professor will probably mark points off regardless of whether or not it was necessary.

Answer 3

1 + cos(x+1)

Answer 4

1+cos(x+1)

Answer 5

f(x)= x+ sin (x+1)

f'(x) = 1 + cos(x + 1)

Answer 6

Iam feeling of your mathematics knowledge.

differentiation is a simple thing if you understand the concept.

let us come into your simple question.

d/dx(x+sin9x=1)



first diff x and sin(x+1) separately(because if two functions are separated by + or - sign).



we know that d/dx(x)=1.



now diff sin(x+1).



in this there are 2 functions sin( ) and x+1.

first diff sin( ).

d/dx(sin(x))= cos(x).

=> d/dx(sin(x+1))=cos(x+1).



=>d/dx(x+1)=1+0.

since d/dx(x)=1 and d/dx(constant(numbers))=0.



therefore

d/dx(x+sin(x+1))=1+cos(x+1)*1.



this is simple if u understand.

if u still feel troublesome contact me

[e-mail]

Answer 7

Use implicit differentiation. in simple terms comprehend that y is an unknown function of x. Given: sin(x + y) + sin(x - y) = a million define u = x + y v = x - y Re-build: sin(u) + sin(v) = a million Take by-product term-by utilising-term: cos(u) du/dx + cos(v) dv/dx = 0 Derivatives of substitutions: du/dx = a million + dy/dx dv/dx = a million - dy/dx as a consequence: cos(x + y)*(a million + dy/dx) + cos(x - y)*(a million - dy/dx) = 0 define D = dy/dx. as a consequence: cos(x + y)*(a million + D) + cos(x - y)*(a million - D) = 0 resolve for D: D = (cos(x + y) + cos(x - y))/(cos(x - y) - cos(x + y)) end: dy/dx = (cos(x + y) + cos(x - y))/(cos(x - y) - cos(x + y))

Answer 8

f ' (x) = 1 + cos(x+1) * {d/dx (x+1)} = 1 + cos(x+1)

Answer 9

f'(x)= 1+cos(x+1)

hope that helps