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Find the implicit derivative $\frac{d}{dx}\left(\sin\left(x\right)+7\cos\left(14y\right)\right)=2$

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Solution

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Final answer to the problem

$y^{\prime}=\frac{2-\cos\left(x\right)}{-98\sin\left(14y\right)}$
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Step-by-step Solution

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  • 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
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1

The derivative of a sum of two or more functions is the sum of the derivatives of each function

Learn how to solve advanced differentiation problems step by step online.

$\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(7\cos\left(14y\right)\right)=2$

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Learn how to solve advanced differentiation problems step by step online. Find the implicit derivative d/dx(sin(x)+7cos(14y))=2. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of the linear function is equal to 1.

Final answer to the problem

$y^{\prime}=\frac{2-\cos\left(x\right)}{-98\sin\left(14y\right)}$

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Function Plot

Plotting: $y^{\prime}=\frac{2-\cos\left(x\right)}{-98\sin\left(14y\right)}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
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.
(◻)
+
-
×
◻/◻
/
÷
◻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

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Main Topic: Advanced differentiation

They are the more complex rules of differentiation. Those include the implicit and logarithmic differentiation.

Used Formulas

See formulas (5)

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