Find the implicit derivative of $-2x-21\ln\left(-x+10\right)=y$

Step-by-step Solution

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Final answer to the problem

$y^{\prime}=-2+\frac{21}{-x+10}$
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Step-by-step Solution

How should I solve this problem?

  • Solve by implicit differentiation
  • Find the derivative using the definition
  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
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Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

$\frac{d}{dx}\left(-2x-21\ln\left(-x+10\right)\right)=\frac{d}{dx}\left(y\right)$

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$\frac{d}{dx}\left(-2x-21\ln\left(-x+10\right)\right)=\frac{d}{dx}\left(y\right)$

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Learn how to solve problems step by step online. Find the implicit derivative of -2x-21ln(-x+10)=y. Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. 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 times a constant, is equal to the constant.

Final answer to the problem

$y^{\prime}=-2+\frac{21}{-x+10}$

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Function Plot

Plotting: $y^{\prime}=-2+\frac{21}{-x+10}$

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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

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