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Mathematics

Higher derivatives

1. Calculate the first four derivatives of the following function:

vyssie-derivacie-1z

Solution:

vyssie-derivacie-1r

2.Calculate the first four derivatives of the following function:

vyssie-derivacie-2z

Solution:

vyssie-derivacie-2r

 

3. Calculate the first four derivatives of the following function:

vyssie-derivacie-3z

Solution:

vyssie-derivacie-2r

4.Calculate the first four derivatives of the following function:

vyssie-derivacie-4z

Solution:

vyssie-derivacie-4r

5. Calculate the first four derivatives of the following function:

vyssie-derivacie-5z

Solution:

vyssie-derivacie-5r

6. Calculate the first three derivatives of the function:

y = ex.sinx

Solution:

vyssie-derivacie-6.gif

7.Calculate the first three derivatives of the function:

vyssie-derivacie-7z

Solution:

vyssie-derivacie-7r

8. Calculate the first three derivatives of the function:

y=sin 2x

Solution:

vyssie-derivacie-8

9.Calculate the first three derivatives of the function:

vyssie-derivacie-9z

Solution:

vyssie-derivacie-9r

10.Show that the function y = excos x satisfies the differential equation 

yIV + 4y = 0

Solution:

 vyssie-derivacie-10

The function y = excos x satisfies the differential equation yIV + 4y = 0