What is the derivative of (x-sqrt(x)+6x^4^3) ?

The derivative of (x-sqrt(x)+6x^4^3) is

What is the first derivative of (x-sqrt(x)+6x^4^3) ?

The first derivative of (x-sqrt(x)+6x^4^3) is

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\frac{d}{d x} ((x - x + 6 x^{4})^{3})

2592 x^{11} + 972 x^{8} - 864 x^{7} x + 108 x^{5} - 180 x^{4} x + 90 x^{4} + 3 x^{2} - 6 x x + 6 x - 54 x^{\frac{15}{2}} - 18 x^{\frac{9}{2}} + \frac{3 ( - x ^{\frac{3}{2}} - x )}{2}

Solution steps

\frac{d}{d x} ((x - x + 6 x^{4})^{3})

Apply the chain rule:

3 (x - x + 6 x^{4})^{2} \frac{d}{d x} (x - x + 6 x^{4})

= 3 (x - x + 6 x^{4})^{2} \frac{d}{d x} (x - x + 6 x^{4})

\frac{d}{d x} (x - x + 6 x^{4}) = 1 - \frac{1}{2 x} + 24 x^{3}

= 3 (x - x + 6 x^{4})^{2} (1 - \frac{1}{2 x} + 24 x^{3})

Simplify

3 (x - x + 6 x^{4})^{2} (1 - \frac{1}{2 x} + 24 x^{3}) : 2592 x^{11} + 972 x^{8} - 864 x^{7} x + 108 x^{5} - 180 x^{4} x + 90 x^{4} + 3 x^{2} - 6 x x + 6 x - 54 x^{\frac{15}{2}} - 18 x^{\frac{9}{2}} + \frac{3 ( - x ^{\frac{3}{2}} - x )}{2}

= 2592 x^{11} + 972 x^{8} - 864 x^{7} x + 108 x^{5} - 180 x^{4} x + 90 x^{4} + 3 x^{2} - 6 x x + 6 x - 54 x^{\frac{15}{2}} - 18 x^{\frac{9}{2}} + \frac{3 ( - x ^{\frac{3}{2}} - x )}{2}

What is the derivative of (x-sqrt(x)+6x^4^3) ?
The derivative of (x-sqrt(x)+6x^4^3) is
What is the first derivative of (x-sqrt(x)+6x^4^3) ?
The first derivative of (x-sqrt(x)+6x^4^3) is