Use the Chain Rule to find dz/dt. dz dt || z = √√√ 1 + x² + y², x = 2 In(t), y = cos(t) 1 √1+ (Int)² + cos² (1) In(t) t - sin(t) cos(t) X

Q: Use the chain rule to find dw dt dw dt W = In (√x² + y² + z²), x = 9 sin(t), y = 8 cos(t), z = 5…

A: W=lnx2+y2+z2 x=9 sin(t) y=8 cos(t) z=5 tan(t)

Q: Let r(t) = (sin t, 2 cos t), t = (a) Find r'(t). (b) Find T(t).

A:

Q: Let P(x) dt. Evaluate 2 | P(x)dx. sin

A:

Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: Let f"(t) = /t – 2 cos t. Determine a general f(t). -

A: Given : f'''t = t - 2cost

Q: Let r(t) = cos(t) i + 4 ln(t² + t)j + 5 tan¯¹(t) k. Find 7' (t).

A:

Q: 5. Given F(x) = cos (t) dt, determine F'(x). 2

A: Using leibniz rule  Explanation is given below....

Q: Using the substitution t = tan(), the integral 2 dx sin(x) – 78 cos(x) can be written as dt 39 – t-…

A: To make substitution and re write the given Integral.

Q: SOLVE BY LINEAR METHOD - y'- 3 X Y = x 3 cos (x)

A:

Q: Y : = x COS -1 x – V1 - x2

A: Given function :

Q: y = In(x² + 4)

A: