What is the derivative of x/(a^2sqrt(a^2+x^2)) ?

The derivative of x/(a^2sqrt(a^2+x^2)) is 1/((a^2+x^2)sqrt(a^2+x^2))

What is the first derivative of x/(a^2sqrt(a^2+x^2)) ?

The first derivative of x/(a^2sqrt(a^2+x^2)) is 1/((a^2+x^2)sqrt(a^2+x^2))

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\frac{d}{d x} (\frac{x}{a ^{2} a ^{2} + x ^{2}})

\frac{1}{( a ^{2} + x ^{2} ) a ^{2} + x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{a ^{2} a ^{2} + x ^{2}})

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{1}{( a ^{2} + x ^{2} ) a ^{2} + x ^{2}}

\frac{d}{d x} (25 ln (x^{2}) - x^{2})

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 4)^{5})

\int_{1}^{4} x d x

\int e^{- 5 x} x d x

\frac{d y}{d x}, x^{\frac{2}{3}} + y^{\frac{2}{3}} = 3

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