Find the derivative of the n^th order of the function y = sinx

a) cos (nπ + x)

b) sin (nπ +x)

c)

d)

Find the derivative of the n^th order of the function y = sin5x cos2x

Find the derivative of the n^th order of the function y = sinx cosx

a)

b)

c)

d)

Find the derivative of the n^th order of the function

y = ln (x² + x − 2) 

a)

b)

c)

d)

a)

b) -

c)

d)

a)

b)

c)

d)

Find the derivative of the second order of the function
 

Find the derivative of the second order of the function
 

Find the derivative of the second order of the function

Given the function
y =  
show that the function satisfies the equation
 

Using the expansion into linear combination of simpler functions find the derivative of the 100^th order of the function
 

Using the expansion into linear combination of simpler functions find the derivative of the 100^th order of the function
 

Prove that if f(x) has a derivative of the n^th order, then

For the function , find 

For the function
 

For the function
 

Using the rule for differentiation of an inverse function, find the derivative  for the function  

Using the rule for differentiation of an inverse function, find the derivative  for the function  

Using the rule for differentiation of an inverse function, find the derivative  for the function  

For the function represented parametrically find the derivative of the first order of y with respect to x
x = a (t – sin t), y = a (1 – cos t)

a)

b)

c) cos t

d) sin t

For the function represented parametrically find the derivative of the first order of y with respect to x

x = k sin t – sin kt, y = k cos t + cos k t

a) cotkt

b)

c)

d) – tan kt

For the function represented parametrically find the derivative of the first order of y with respect to x
x = 2 ln cot t, y = tan t + cot t

a) cot2t; , k ε ℝ

b) tan2t; , k ε ℝ

c) cott; t ≠ kπ, k ε ℝ

d) tant; , k ε ℝ

For the function represented parametrically find the derivative of the first order of y with respect to x
x = , y =

a) – c

b) c

c)

d)  c