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

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

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isaaq
3 months ago
Sin 3A = 3 Sin A - 4 sin³A.
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..
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victory
3 months 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
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isaaq
3 months ago
just use the chain rule
y = sin(3x^2)
y' = cos(3x^2)(6x)
y" = -sin(3x^2)(6x)^2 + cos(3x^2)(6)
y"' = -cos(3x^2)(6x)^3 - sin(3x^2)(2*6x)(6) - sin(3x^2)(6x)(6)
I'll let you do the algebra.
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