Can someone help me to find this:
Find the partial derivatives of the first order of u = x ^ 2 * sin (√ y + z))

Question

Can someone help me to find this:
Find the partial derivatives of the first order of u = x ^ 2 * sin (√ y + z))

jusaquikie · Answer

ok this is easier than it sounds, basicly take the derivitive of the function 3 times, once with respect to x once with respect to y and once with respect to z so du/dx = 2x*sin(sqrt(y+z))
everything without an x is treated like a constant. repeat for the other two variables id du/dy and du/dz

anonymous · Answer

Thanks, i understand the concept but doing du/dy diffucult for me..can you do and post please..

jusaquikie · Answer

of the x² is just a constant and it comes along for the ride z just just like a number so lets' replace it with 1 for now just to get a better understanding so what we are taking the derivative of is $$\sin(\sqrt{y+1})$$

jusaquikie · Answer

$$\cos(\sqrt{y+1})*(y+1)^(-1/2)*1$$

anonymous · Answer

du/dy =x²cos(sqrt(y+1)/2(sqrt(y+1) is this correct?

jusaquikie · Answer

well the replacing part made it look messier so i'll put the x² and z back$$x^2\cos(\sqrt{y+z})*\frac{1 }{ \sqrt{y+z}}$$

jusaquikie · Answer

it doesn't like the 1/2 power

jusaquikie · Answer

your right i left off the 2 on the bottom

anonymous · Answer

Thanks friend for your help...can you do second d²u/dy²??

jusaquikie · Answer

so it can be rewritten as $$\frac{ x^2 }{2\sqrt{y+z} }\cos(\sqrt{y+z})$$

anonymous · Answer

good!!
 thanks i understood this part...

jusaquikie · Answer

can't i need to go to bed but you can see the steps, if it's not the varible that you are working on treat it like a constant

jusaquikie · Answer

the second derivative is just differentiating the answer we just derived using the same steps.

anonymous · Answer

Thanks..