1. calculators
  2. Inverse Trigonometric Functions Differentiation

Inverse trigonometric functions differentiation Calculator

Get detailed solutions to your math problems with our Inverse trigonometric functions differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

Go!
Go!
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

1

Solved example of inverse trigonometric functions differentiation

$\frac{d}{dx}\left(\arcsin\left(4x^2\right)\right)$

Taking the derivative of arcsine

$\frac{1}{\sqrt{1-\left(4x^2\right)^2}}\frac{d}{dx}\left(4x^2\right)$

Multiplying the fraction by $\frac{d}{dx}\left(4x^2\right)$

$\frac{\frac{d}{dx}\left(4x^2\right)}{\sqrt{1-\left(4x^2\right)^2}}$
2

Taking the derivative of arcsine

$\frac{\frac{d}{dx}\left(4x^2\right)}{\sqrt{1-\left(4x^2\right)^2}}$
3

The power of a product is equal to the product of it's factors raised to the same power

$\frac{\frac{d}{dx}\left(4x^2\right)}{\sqrt{1-16x^{4}}}$
4

The derivative of a function multiplied by a constant ($4$) is equal to the constant times the derivative of the function

$\frac{4\frac{d}{dx}\left(x^2\right)}{\sqrt{1-16x^{4}}}$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{4\cdot 2x^{\left(2-1\right)}}{\sqrt{1-16x^{4}}}$

Subtract the values $2$ and $-1$

$\frac{4\cdot 2x^{1}}{\sqrt{1-16x^{4}}}$

Multiply $4$ times $2$

$\frac{8x^{1}}{\sqrt{1-16x^{4}}}$

Any expression to the power of $1$ is equal to that same expression

$\frac{8x}{\sqrt{1-16x^{4}}}$
5

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{8x}{\sqrt{1-16x^{4}}}$

Final Answer

$\frac{8x}{\sqrt{1-16x^{4}}}$

Struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!