What is the derivative of x/(sqrt(1-4x^2)) ?

The derivative of x/(sqrt(1-4x^2)) is 1/((1-4x^2)sqrt(1-4x^2))

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

The first derivative of x/(sqrt(1-4x^2)) is 1/((1-4x^2)sqrt(1-4x^2))

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\frac{d}{d x} (\frac{x}{1 - 4 x ^{2}})

\frac{1}{( 1 - 4 x ^{2} ) 1 - 4 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{1 - 4 x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} 1 - 4 x ^{2} - \frac{d}{d x} ( 1 - 4 x ^{2} ) x}{( 1 - 4 x ^{2} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (1 - 4 x^{2}) = - \frac{4 x}{1 - 4 x ^{2}}

= \frac{1 \cdot 1 - 4 x ^{2} - ( - \frac{4 x}{1 - 4 x ^{2}} ) x}{( 1 - 4 x ^{2} ) ^{2}}

Simplify

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

= \frac{1}{( 1 - 4 x ^{2} ) 1 - 4 x ^{2}}

\frac{\partial}{\partial y} (y^{2} ln (x))

x \to 1 + lim (\frac{x - 2}{x - 1})

\frac{\partial}{\partial y} (x^{2} + y^{4})

\int cot (x) csc^{2} (x) d x

\int cot (\frac{x}{5}) d x

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