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Find the implicit derivative of $2y+3x=7$

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Solution

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Final answer to the problem

$y^{\prime}=-\frac{3}{2}$
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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
  • Load more...
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1

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

$\frac{d}{dx}\left(2y+3x\right)=\frac{d}{dx}\left(7\right)$

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

$\frac{d}{dx}\left(2y+3x\right)=\frac{d}{dx}\left(7\right)$

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Learn how to solve differential calculus problems step by step online. Find the implicit derivative of 2y+3x=7. Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the constant function (7) is equal to zero. 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

$y^{\prime}=-\frac{3}{2}$

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Function Plot

Plotting: $y^{\prime}=-\frac{3}{2}$

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1
2
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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
D□x
∫
∫◻
|◻|
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:

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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

See formulas (4)

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