2x f(x) sec(t*) dt. %3D -2x

Q: Find the domain and range for f(x, y) = y² /x³ – y.

A: The given function is: f(x,y)=y2x3-y Now, the function is defined for all y but if  x3-y≥0⇒x3≥y⇒x≥y3…

Q: y = 4x° + 4x at (1, 2)

A:

Q: Compute the derivative:

A: Given, ddx∫0x4+t6 dt

Q: f(x, y) = x".

A: Given: f(x,y)=xy To find the partial derivative with respect to x of a function of two variables…

Q: Find the derivative of the function y = x²e*

A:

Q: y = vx %3D

A:

Q: z = Vx4 + yf, fz (1, 2)

A:

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: 6) Find The derivative of yo

A:

Q: Find the derivative of ƒ (æ) = (8x (8z4 – 32 30)°. f' (z) =

A: Given,

Q: Calculate the derivative: + (2t3 – 9t) dt = dz

A: Evaluate the given derivative as follows. ddx∫0x2t3-9tdt=ddx2t44-9t220x=ddx2x44-9x22-0

Q: Approximate the derivative of y=x at x=1 by forming small changes.

A: SOLUTION:-

Q: Find the derivative of f(w) = √3w²

A:

Q: Find the derivative of 1-3)* (t3 -8) ,t # 2 2-t

A: Explanation of the answer is as follows

Q: Find the derivative: n[(x³ + 2) (x² + 3)]. Evaluate S dx. Зx8 — 2 2x*- x2 Evaluate dx.

A:

Q: 8. y = (3x² + 7)²

A: y=(3x2+7)2

Q: Calculate the derivative: d dx * ST (6t3 – 9t) dt = -

A:

Q: -1 8y ¹ ($) ₁ f(x, y) = tan¯ (Duf) p = ху + 5 sin¯¹ (XY), P = (64, 8), u = 7i+6j 1024

A: Given: f(x,y)= tan-1(8y/x)+ 5Sin-1(xy/1024) Point P(64,8) Vector u= 7i+6j

Q: Calculate the derivative at the point (0,0) of the function given by the equation x=y−2siny.

A: We differentiate both sides with respect to x

Q: Find the derivative using the long method 3 u = t2

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: