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Find the implicit derivative $\frac{d}{dx}\left(\tan\left(y\right)=x^2y^2+2x\right)$

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Solving: $\frac{d}{dx}\left(\tan\left(y\right)=x^2y^2+2x\right)$
Solve instead: $\frac{dy}{dx}\left(\tan\left(y\right)=x^2y^2+2x\right)$

Solution

Final answer to the problem

$y^{\prime}=\frac{2xy^2+2}{\sec\left(y\right)^2-2x^2y}$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

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

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

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(tan(y)=x^2y^2+2x). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. 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.

Final answer to the problem

$y^{\prime}=\frac{2xy^2+2}{\sec\left(y\right)^2-2x^2y}$

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Function Plot

Plotting: $y^{\prime}=\frac{2xy^2+2}{\sec\left(y\right)^2-2x^2y}$

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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

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