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Find the derivative of $\arcsin\left(\sqrt{9-5x^2}\right)$

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{-5x}{\sqrt{-8+5x^2}\sqrt{9-5x^2}}$
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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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1

Taking the derivative of arcsine

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

$\frac{1}{\sqrt{1-\left(\sqrt{9-5x^2}\right)^2}}\frac{d}{dx}\left(\sqrt{9-5x^2}\right)$

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Unlock the first 3 steps of this solution

Learn how to solve integral calculus problems step by step online. Find the derivative of arcsin((9-5x^2)^(1/2)). Taking the derivative of arcsine. Cancel exponents \frac{1}{2} and 2. Simplify the product -(9-5x^2). Subtract the values 1 and -9.

Final answer to the problem

$\frac{-5x}{\sqrt{-8+5x^2}\sqrt{9-5x^2}}$

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Function Plot

Plotting: $\frac{-5x}{\sqrt{-8+5x^2}\sqrt{9-5x^2}}$

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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
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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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