C) f(x,y) = 3y/2x2
Partial derivative wrt "X"
f(x,y) = 3y d(1/2x2)/dx
f(x,y) = 3y (-2 x(-2-1)/2)
f(x,y) = -3y/x3
d) f(x,y) = 2yx ln(x)
Partial derivative wrt x
f(x,y) = 2y d(x lnx)
f(x,y) = 2y (x (d(lnx)/dx) + lnx (d(x)/dx )
f(x,y) = 2y ( x(1/x)+ lnx)
f(x,y) = 2y (1+lnx)
e) f(x,y) = (2x+y-yx2)/2x
f(x,y) = 1 - (yx/2) + (y/2x)
Partial derivative wrt x
f(x,y) = (d(1)/dx )+ (d(y/2x)) -( d(yx/2)/dx)
f(x,y) = 0 + (-y x(-1-1)/2) - (y/2)
f(x,y) = (--y/2x2)+(--y/2)
Q1) Evaluate the partial derivative with respect to x of each of the following functions d)...
Q1) Evaluate the partial derivative with respect to z of each of the following functions. a) f(x, y) 7r2y
(3) Practice Math (a) Find the partial derivative of CAť)(yb) with respect to x ( yb) = a In x + blny (c) Take the derivative of f(x)-h(x)g(x) with respect to r (d) What is the partial derivative of y-kθη1-9 with respect to k (e) Solve for N when No-1 (f) What is the partial derivative of In(w + 2N) with respect to N b) Show that Tn (Ta 01-0
Find the first derivative with respect to the domain variable for the following functions. 4. f(x) = (x - 2)(x² + 2x +4)
A derivative with respect to the same variable can be taken more than once: partial differential/partial differential x(partial differential F/partial differential x) partial differential^2 F/partial differential x^2 and is called the second derivative off. Evaluate the following expressions, assuming the ideal gas law applies. (a) (partial differential^2V/partial differential p^2)_n, T (b) (partial differential^2 rho/partial differential T^2)_n, v
Question 6 10 points Save Ans Determine the partial derivative of the following function with respect to "z" and evaluate at point A:(-3,4,-2): f(x, y, z) = axºyz+b yºxz+cz*yx Uses the following values: a=4; b=3; and c=1.
4. Find the partial derivative of the following equation with respect to x and y:
5. Find the derivative of the following functions without writing down a single partial derivative. (a) f:R4R2x2 defined by に디2+1: 디.X2 + X". f(x, y, z, w) - 5. Find the derivative of the following functions without writing down a single partial derivative. (a) f:R4R2x2 defined by に디2+1: 디.X2 + X". f(x, y, z, w) -
6 A Find the derivative of each of the following functions using derivative rules. Remember to SIMPLIFY first! Show all steps for full marks <2 mks each> Differentiate each of the following equations. Be sure to write proper notation. y = 7x6 + 10x4 - 8x - 5 $(x)= V1 f (x) = 7 y = 4x®(3x6 - 2x) f (x) = - s(t)= _4° +56 f(x)g(x)h(x) cf(x) f(x) + g(x)
Find the derivative of the following functions: Inx 22 C. a. F(x) = In (3x) b. Y=: Y=52x-1 d. Y= log1032 e. Y=In(x2-2)2/3 f. Y= In g. Y= log2 (2x - 1) h. Y= 8** e 1+e+
Which of the below functions is a solution to the following partial differential equation? a2f ay2 - Hint: For each function below, calculate both sides of the above equation, subtract, and then simplify. Note: It is possible that more than one of the below functions will satisfy the above equation. If that is the case, then selecting any one of the functions that work will give you full marks. (F) X«-» (A) 2-256x sin 8y (B) 2 Ince' + %)...