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

Q: y = 4x° + 4x at (1, 2)

A:

Q: y = vx %3D

A:

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

A:

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: 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

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: