hi, i am trying to fin the derivative of y= pi^2 + e^x + x^2 + x^x^(1/2) at x=1. Help please!! :)

Question

hi, i am trying to fin the derivative of y= pi^2 + e^x  + x^2 + x^x^(1/2) at x=1. Help please!! :)

anonymous · Answer

Which part do you not know how to differentiate?

amistre64 · Answer

$$y= \pi^2 + e^x + x^2 + x^{x^(1/2)}$$ this?

amistre64 · Answer

pi^2 is a constant it goes to 0

e^x derives to e^x

x^2 derives to 2x

and x^(x^(1/2)) is the tricky one

amistre64 · Answer

$$x^{x^{1/2}}=x^{(1/2)x}$$

anonymous · Answer

$$y=\pi^2+e^x+x^2+x^\sqrt{x}$$
First, remove the constants, then individually differentiate each part separated by + signs. Differentiate each part individually, and use logarithmic differentiation for the last part.

amistre64 · Answer

id assume it goes:

$$Dx(x^{(1/2)x}) \implies \frac{1}{2}*\frac{x}{2}(x)^{\frac{x-2}{2}}$$

amistre64 · Answer

$$\frac{x*x^{(x-2)/2}}{4}$$

and the top simplifies further since like bases add exponents

amistre64 · Answer

but if x = 1; we dont need to go thru all the window dressing do we :)

anonymous · Answer

$$y=x^\sqrt{x}$$
$$\ln(y)=\sqrt{x}\ln(x)$$
$$Dx(\ln(y)=\sqrt{x}\ln(x))$$
$$y'/y = 1/2 *1/\sqrt{x} * \ln(x) + \sqrt{x}/x $$
$$y' = (1/2 *1/\sqrt{x} * \ln(x) + \sqrt{x}/x) /y $$
$$y' = (1/2 *1/\sqrt{x} * \ln(x) + \sqrt{x}/x) /x^\sqrt{x} $$
Into which, you could plug 1.