Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

Q: Show that cosh r d tanh-(sinh r) dr %3D 2 – cosh?(r) Show that the derivative of y = x* inh= is…

A: Please find the detailed proof.

Q: 11. Use implicit differentiation to determine dx dy given: x*(x + y) = y²(3x – y) %3D

A:

Q: sec?x Integral tanx

A:

Q: dy Find dx of xy = x + cot y

A: The given equation is xy=x+cot y  Differentiate both sides  ddxxy=ddxx+ddxcot y y+xdydx=1-csc2ydydx…

Q: Differentiate y = tanh 2x + coth x A. 2 B. 2 (tanh 2x) C. 2 (sech22x + csch²2x) D. 2 (sech2x –…

A:

Q: Find dy/dx for the equation y^2+xy=1

A: Given:

Q: Differentiate implicitly to find dx Зху + 5 3 0 dy %3D dx

A:

Q: d arctan (tanh x) dx Show that sech 2.x.

A:

Q: Find of xy = cot(xy) dx

A:

Q: Find dy/dx for y = x*, x>0.

A:

Q: given y=x^3 Inx,dy/dx is

A: Note:- Here we consider your given equation is y=x3lnx instead of y=x3In(x) because In(x) is not a…

Q: INIL Find in sin (1 + 2x) + xy = ecosy dy dx

A: We need to find derivative.

Q: Find for y = dx dy dx 1 C

A: On solving this we will get

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: If y = tanh-¹ (cosz), show that d'y dy (tanz) + dr2 da = 0.

A:

Q: 2/ Find dy To y=sin h'(tanx) 2-y (X+1)}

A:

Q: what is dy/dx of x+ylny=y+xlnx+1

A: Given,          x+ylny=y+xlnx+1

Q: Find dy Ldx For the following (Jy)' =(In tan x)(x") ( sin x)"

A:

Q: Find the following antiderivatives. a. ∫(3x^4-cosx)dx b. ∫(5^3sqrt(x^2) + 2x-1)dx c.…

A: ∫xn dx = xn+1n+1+C. ∫ax dx = axloga+C

Q: cosh x dy + (y sinh x + ex) dx = 0

A: Step 1:

Q: Find dy/dx by implicit differentiation   x Sin y +y sin x = 1

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.