What is the derivative of sqrt(5/(x+1)-x^4) ?

The derivative of sqrt(5/(x+1)-x^4) is -(sqrt(5))/(2(x+1)^{3/2)}-4x^3

What is the first derivative of sqrt(5/(x+1)-x^4) ?

The first derivative of sqrt(5/(x+1)-x^4) is -(sqrt(5))/(2(x+1)^{3/2)}-4x^3

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

What is the derivative of sqrt(5/(x+1)-x^4) ?
The derivative of sqrt(5/(x+1)-x^4) is -(sqrt(5))/(2(x+1)^{3/2)}-4x^3
What is the first derivative of sqrt(5/(x+1)-x^4) ?
The first derivative of sqrt(5/(x+1)-x^4) is -(sqrt(5))/(2(x+1)^{3/2)}-4x^3