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Popular >

derivative of 6arcsin(x^2)

Solution

\frac{d}{d x} (6 arcsin (x^{2}))

Solution

\frac{12 x}{1 - x ^{4}}

Solution steps

\frac{d}{d x} (6 arcsin (x^{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (arcsin (x^{2}))

Apply the chain rule:

\frac{1}{1 - ( x ^{2} ) ^{2}} \frac{d}{d x} (x^{2})

= \frac{1}{1 - ( x ^{2} ) ^{2}} \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{2}) = 2 x

= 6 \cdot \frac{1}{1 - ( x ^{2} ) ^{2}} \cdot 2 x

Simplify

6 \cdot \frac{1}{1 - ( x ^{2} ) ^{2}} \cdot 2 x : \frac{12 x}{1 - x ^{4}}

= \frac{12 x}{1 - x ^{4}}

Popular Examples

derivative of f(x)=x-1/(x^2)derivative of

f (x) = x - \frac{1}{x ^{2}}

integral of 9+9tan^2(x)

\int 9 + 9 tan^{2} (x) d x

derivative of x(7x+9^{1/3})

\frac{d}{d x} (x (7 x + 9)^{\frac{1}{3}})

integral of (3x^2)/4

\int \frac{3 x ^{2}}{4} d x

(\partial)/(\partial x)(e^{(x-1)^2})

\frac{\partial}{\partial x} (e^{(x - 1)^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of 6arcsin(x^2) ?
The derivative of 6arcsin(x^2) is (12x)/(sqrt(1-x^4))
What is the first derivative of 6arcsin(x^2) ?
The first derivative of 6arcsin(x^2) is (12x)/(sqrt(1-x^4))