B) prove du d 1. sec u = secu tan u %3D dx dx

Q: 10)Use implicit differentiation to find dy/dx

A:

Q: 2 [(3 sec2 x + - x)dx 4

A: Integrate

Q: Find the derivatives of the functions in Exercis

A: Given function is: y=1x sin-5 x-x3 cos3 x We have to find dydx.

Q: hpxp(₂h + x)us hx [V² [V² Find

A:

Q: S tan — х) dx

A: To integrate: ∫tan(x4-x)dx Solution: Given, ∫tan(x4-x)dx On simplifying further we get:…

Q: d (sec x) show that secx tan x. dx

A:

Q: sect (x) dx[ by two methods

A:

Q: Describe the technique for finding ∫ sec5 x tan7 x dx. Do not integrate.

A: Given ∫sec5x tan7x dx

Q: If sin t sint + cost A = tant A + tant then

A: if sin tsin t+cos t=tan tA+tan t

Q: -1 du 4) [cot-u] %3D 1+u2 dx dx d 5) 1 du [sec-1 u] %3D dx u vu2-1 dx -1 du 6) [csc-1 u] dx u vu2-1…

A:

Q: If fo =sinax find f'x)

A: Finding the derivative of the function using chain rule of differentiation

Q: Evaluate and Graph ¹) S ( sin x (1-x) dx dy do

A: Given: ∫01∫0ysinx11-xdxdy. To Evaluate: The above integral. To Sketch: the graph of the region of…

Q: m) -dx 1+sin(2x)

A:

Q: 7) | sec x. dx

A: Given:       ∫ sec5x dx

Q: sec Vn du in

A:

Q: Let 5 sin⁡x+ 7 cos⁡ y=6. dy/dx= d^2y/dx^2

A: 5sinx+7cosy=6Differentiate w.r.t x5cosx-7sinydydx=05cosx=7sinydydxdydx=5cosx7siny

Q: sinx Show that -dx = sinx + cosX 2

A: Given, ∫0π2sinxsinx+cosx dxFormula→∫0afx dx=∫0afa−x dx

Q: DO NOT include spaces in between characters. * Determine the range of y =3 sin 4x+1.

A: Topic:- function

Q: (sin°x dx

A:

Q: Find all Second partial derivatives fcx.y)- Sin?Cmx+ny)

A: Given that, f(x, y) = sin2(mx + ny) we have to find second partial derivative with respect to x and…