If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

Q: f(x)=x+5 glx)=x -1

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Q: If xy? - y3 = 5, find y'. y' =

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Q: Find dy/dx for  A) y=43x  B) y=e7x(^3)+5 the ^3 is an exponent, sorry!

A: To determine the derivative of the function.

Q: 3. Sxe**(4** – e)dx

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Q: Find dy -, if dx dy dx y = u U³ || - u and u = 4x² + 1.

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Q: Write down a formula for ∂z/∂y if z is defined implicitly as a function of x and y by the equation…

A: The given equation is yz=e3x+z.

Q: b) y = In(xeVx + 2)

A: The solution are next step..

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: here w

A: Here we have,  z(w)=w23w+cewz(w)=w23+1+cw23ewz(w)=w53+cw23ew differentiate with respect to w

Q: y"+y=sec³x

A: The given equation is: y"+y=sec3x

Q: Evaluate Sm e" dæ. • 2 does not exist (diverges)

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Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5