S (x, y) = sen (r² – 0²) + In(r® + 0), con Vr? + y? A r = = arctan

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: a2f, a2f ду? Q1: A- Show that + = 0, where f(x, y) = In(x? + y?) + tan-(2) %3D

A:

Q: find dylde O x+ tanxy =D0

A: In the question it is asked to calculate derivative of x+tan(xy)=0 with respect to x.…

Q: Find y in terms of x. dy = x 2 + 5, curve passes through (0, 14) dx x3 A) y = + 5x 3 B y = x3 + 5x +…

A:

Q: f(x.y) = 7x?y",camate and af and ,campute

A: Given fx,y=7x2y4we have to find ∂f∂x =?    and   ∂f∂y=?

Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

Q: Evaluate r(2) and r(-1) for r(t) = (sin 1,12, (1² + 1)~1). %3D

A:

Q: daffəx and åf/ðy y) = x² – xy + y² v) = sin? (x – 3y)

A:

Q: (2y + √y sin x) dx + xdy = 0

A:

Q: and p(n) iF IF Fon) = 4 sec t dz.

A:

Q: dy Differentiate implicitly to find dx exy 2x+9y+3

A:

Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

A:

Q: Find V· (V × F), if F(x, y, z) = 3ei+ 4.xe®j – 2ev²k. V·(V × F) =

A: We need to find dot product.

Q: Find fur for f(x, y) = 7xe* y° sin (/x - 3x* +1)+9x°e"

A:

Q: 3 tari' (xty) , Prane that x2+ ydz Sen 2z be

A: We have z=tan-1x+yx-y This implies tanz=x+yx-y Let u=tanz Then we first need to find the degree of…

Q: Cosx 2) ). y dx+ týž - Sinx (²) dy = уч

A: