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# Find the derivative $\frac{d}{dx}\left(x+\sin\left(x\right)+\frac{\tan\left(x\right)}{x}\right)$ using the sum rule

## Step-by-step Solution

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### Videos

$1+\cos\left(x\right)+\frac{x\sec\left(x\right)^2-\tan\left(x\right)}{x^2}$
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## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(x+\sin\left(x\right)+\frac{\tan\left(x\right)}{x}\right)$

Specify the solving method

1

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(\frac{\tan\left(x\right)}{x}\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(\frac{\tan\left(x\right)}{x}\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(x+sin(x)(tan(x)/x) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function is equal to 1. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}.

$1+\cos\left(x\right)+\frac{x\sec\left(x\right)^2-\tan\left(x\right)}{x^2}$
SnapXam A2

### beta Got another answer? Verify it!

Go!
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0
a
b
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g
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u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\frac{d}{dx}\left(x+\sin\left(x\right)+\frac{\tan\left(x\right)}{x}\right)$

### Main topic:

Sum Rule of Differentiation

~ 0.07 s