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

Step-by-step Solution

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asinh
acosh
atanh
acoth
asech
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Final Answer

$\frac{-e^{\frac{-x}{y}}}{y}$
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Step-by-step Solution

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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.

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

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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 -1.

Final Answer

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

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 derivative of e^(-1x/y) using the product ruleFind derivative of e^(-1x/y) using the quotient ruleFind derivative of e^(-1x/y) using logarithmic differentiationFind derivative of e^(-1x/y) using the definition

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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

How to improve your answer:

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

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