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

The derivative of 4/(x^2+sqrt(x)) is -(2(4xsqrt(x)+1))/(sqrt(x)(x^2+\sqrt{x))^2}

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

The first derivative of 4/(x^2+sqrt(x)) is -(2(4xsqrt(x)+1))/(sqrt(x)(x^2+\sqrt{x))^2}

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derivative of

\frac{4}{x ^{2} + x}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

e^{- x}, 0

\frac{d}{d x} ((2 x + 5) (3 x^{2} - 4 x + 1))

(x + 1) (ln (x + 1))

e^{2 x}, e^{5 x}, x = 1

\frac{\partial}{\partial x} (x 1 + y^{9})

What is the derivative of 4/(x^2+sqrt(x)) ?
The derivative of 4/(x^2+sqrt(x)) is -(2(4xsqrt(x)+1))/(sqrt(x)(x^2+\sqrt{x))^2}
What is the first derivative of 4/(x^2+sqrt(x)) ?
The first derivative of 4/(x^2+sqrt(x)) is -(2(4xsqrt(x)+1))/(sqrt(x)(x^2+\sqrt{x))^2}