Question

Solve Calculus .. Answer if u only know or will be deleted by mod

Answer 1

We are looking for the derivative of $y=\dfrac{x^{5.5}+x}{\sqrt{x}}\,$. 

To make the problem easier, we rewrite fraction on the right using $x^0^.^5$  instead of $\sqrt{x}$. 


$y=\dfrac{x^{5.5}+x}{x^0^.^5}\,$ 

Now split the fraction into the sum of two pieces.

$y=\dfrac{x^{5.5}+x}{x^0^.^5} + \dfrac{x}{x^0^.^5}$ 

We simplify this further using the laws of exponents.

$x=x^5+x^0^.^5$ 

Using the power rule, we differentiate. 

$\dfrac{dy}{dx} = 5x^4+0.5x^-^0^.^5$ 

The standard way to write this is
$\dfrac{dx}{dy} = 5x^4 + \dfrac{1}{2 \sqrt{x} }$

Answer 2

To ease things we have replaced the exponent 5.5 by 11/2

y= (x¹¹/² + x) / √x. Its derivative has the form of (u'v-v'u)/v²

u=(x¹¹/² + x)==> dx/du = 11/2(x⁹/₂) +1

v= √x ===> dx/dv = 1/2√x

dy/dx= {[11/2(x⁹/₂) +1].(√x) - (1/2√x)(x¹¹/² + x)} /x
It can be written (1st simplification):

dy/dx =[(11/2)x⁹/₂ +1]/√x  -  (x¹¹/² + x) / ( 2x√x)

After the final simplification you will get 5x⁴ + 1/2√x