Try now NerdPal! Our new app on iOS and Android

# Find the derivative of $e^{\frac{-x}{y}}$

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
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

###  Videos

$\frac{-e^{\frac{-x}{y}}}{y}$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

$\frac{d}{dx}\left(e^{\frac{-x}{y}}\right)$

Specify the solving method

1

Applying the derivative of the exponential function

$e^{\frac{-x}{y}}\frac{d}{dx}\left(\frac{-x}{y}\right)$

Learn how to solve differential calculus problems step by step online.

$e^{\frac{-x}{y}}\frac{d}{dx}\left(\frac{-x}{y}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of e^((-x)/y). Applying the derivative of the exponential function. The derivative of a function multiplied by a constant (\frac{1}{y}) is equal to the constant times the derivative of the function. The derivative of the linear function times a constant, is equal to the constant. Multiplying the fraction by -e^{\frac{-x}{y}}.

$\frac{-e^{\frac{-x}{y}}}{y}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind d/dx(e^((-x)/y)) using the product ruleFind d/dx(e^((-x)/y)) using the quotient ruleFind d/dx(e^((-x)/y)) using logarithmic differentiationFind d/dx(e^((-x)/y)) using the definition

SnapXam A2

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
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

### Main topic:

Differential Calculus

~ 0.06 s

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account