find the first, second and third derivative of : e^x^4?

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victory

1 week ago

1 week ago

let y=e^x^4

dy/dx=4x^3e^x^4

d^2y/dx^2=12x^2e^x^4+4x^34/dx(e^x^4)

=12x^2e^x^4+4x^3e^x^4*4x^3

=12x^2e^x^4+16x^6e^x^4

d^3y/dx^3=24xe^x^4+12x^2dy/dx(e^x^4)+96x^5e^x^4+16x^6d/dx(e^x^4)

=24xe^x^4+48x^5e^x^4+96x^5e^x^4+64x^9e^x^4

dy/dx=4x^3e^x^4

d^2y/dx^2=12x^2e^x^4+4x^34/dx(e^x^4)

=12x^2e^x^4+4x^3e^x^4*4x^3

=12x^2e^x^4+16x^6e^x^4

d^3y/dx^3=24xe^x^4+12x^2dy/dx(e^x^4)+96x^5e^x^4+16x^6d/dx(e^x^4)

=24xe^x^4+48x^5e^x^4+96x^5e^x^4+64x^9e^x^4

1 week ago

Now write the expression according to the questions requirements..

Sin3x = 3 sinx - 4 sin^3 (x)

Sin^3 x = sin3x -3 sinx ÷(- 4 )

First derivation will be like this..

The first derivatives of sin^3x = (cos3x × 3 - 3 cosx )÷ -4

Now proceed the problem for second derivative you will easily get the answer..