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Find the derivative of $\sqrt{\arccos\left(3x^2\right)}$

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Solution

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Final Answer

$\frac{-3x}{\sqrt{1-9x^{4}}\sqrt{\arccos\left(3x^2\right)}}$
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Step-by-step Solution

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

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

Learn how to solve discriminant of quadratic equation problems step by step online.

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

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Learn how to solve discriminant of quadratic equation problems step by step online. Find the derivative of arccos(3x^2)^1/2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Taking the derivative of arccosine. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant (3) is equal to the constant times the derivative of the function.

Final Answer

$\frac{-3x}{\sqrt{1-9x^{4}}\sqrt{\arccos\left(3x^2\right)}}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of arccos3x^2^0.5 using the product ruleFind derivative of arccos3x^2^0.5 using the quotient ruleFind derivative of arccos3x^2^0.5 using logarithmic differentiationFind derivative of arccos3x^2^0.5 using the definition

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Plotting: $\frac{-3x}{\sqrt{1-9x^{4}}\sqrt{\arccos\left(3x^2\right)}}$

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(◻)
+
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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: Discriminant of Quadratic Equation

Quadratic equations are those algebraic equations of the form ax^2+bx+c, where a, b, and c are constant values. The discriminant of a quadratic equation is calculated using the formula D=b^2-4ac, and it helps us to determine how many roots an equation of this type has. When D>0 the equation has two real roots, when D<0 the equation has no real roots, and when D=0 the equation has a repeated real root.

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