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Find the derivative of $\frac{-x}{y}$ using the definition

Step-by-step Solution

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Final Answer

$\frac{-1}{y}$
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Step-by-step Solution

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Find the derivative of $\frac{-x}{y}$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $\frac{-x}{y}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get

$\lim_{h\to0}\left(\frac{\frac{-\left(x+h\right)}{y}-\frac{-x}{y}}{h}\right)$

Learn how to solve definition of derivative problems step by step online.

$\lim_{h\to0}\left(\frac{\frac{-\left(x+h\right)}{y}-\frac{-x}{y}}{h}\right)$

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Learn how to solve definition of derivative problems step by step online. Find the derivative of (-x)/y using the definition. Find the derivative of \frac{-x}{y} using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \frac{-x}{y}. Substituting f(x+h) and f(x) on the limit, we get. Multiplying the fraction by -1. Simplify the product -(x+h). The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.

Final Answer

$\frac{-1}{y}$

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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 derivdef(-1x/y) using the product ruleFind derivdef(-1x/y) using the quotient ruleFind derivdef(-1x/y) using logarithmic differentiation

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Function Plot

Plotting: $\frac{-1}{y}$

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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: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

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