Question

The Philadelphia Art Museum, due to space issues, is more cautious about A)  Appointing new curators B)  Selling off old art works C)  Construction of new museums D)  Acquisitions and donations of art​

Answer 1

Answer: Derivative of cot x is −cosec2x

We can proceed step by step to find the derivative.

Explanation:

As per trigonometric identities, cot x can also be written as cosx / sinx ------- (i)

Now we can use quotient rule of differentiation to find the derivative of cot x.

d cotx/ dx = d(cosx / sinx)/dx

Quotient rule: d (uv)/ dx ={ ( vdu / dx− udv / dx) / v2}

Here u = cos x, v = sin x

d(cosx / sinx)/dx = [(d (cos x)/dx)sin x − cosx (d(sin x)/ dx )] / sin2x -------- (ii)

We can substitute the formulae for the derivatives of sin x and cos x given by

d(cos x) /dx = −sin x and d(sin x)/dx = cos x

On putting the above values in equation (ii), we get

d(cot x)/dx = {−sin x sin x − cos x cos x } / sin2x

= - (sin2x + cos2x) / sin2x

= −1 / sin2x

= −(cosec2x)

⇒ d(cotx)/dx = −(cosec2x)

So, the derivative of cot x is −cosec2x

Answer 2

Answer:

The City of Philadelphia owns the Museum building, the Rodin Museum building, the Ruth and Raymond G. Perelman building (2501 Benjamin Franklin Parkway) and the two historic houses in Fairmount Park that are operated by the Museum (Mount Pleasant and Cedar Grove).