Find the implicit derivative $\frac{d}{dx}\left(\tan\left(x\right)\right)=0$

Step-by-step Solution

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acosh
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Final answer to the problem

$\sec\left(x\right)^2=0$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Exact Differential Equation
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1

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 ${f'(x) = sec^2(x)\cdot D_x(x)}$

$\frac{d}{dx}\left(x\right)\sec\left(x\right)^2=0$
2

The derivative of the linear function is equal to $1$

$\sec\left(x\right)^2=0$

Final answer to the problem

$\sec\left(x\right)^2=0$

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Function Plot

Plotting: $\sec\left(x\right)^2=0$

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1
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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: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

Used Formulas

See formulas (2)

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