D. Jika Y=X4 carilah dy/dx
Penjelasan dengan langkah-langkah:
• DiferentiaL
we have a function :
y = ( {x}^{4} + 2x)( {x}^{3} + 2 {x}^{2} + 1)y=(x
4
+2x)(x
3
+2x
2
+1)
Let :
u = {x}^{4} + 2x = > frac{du}{dx} = 4 {x}^{3} + 2u=x
4
+2x=>
dx
du
=4x
3
+2
v = {x}^{3} + 2 {x}^{2} + 1 = > frac{dv}{dx} = 3 {x}^{2} + 4xv=x
3
+2x
2
+1=>
dx
dv
=3x
2
+4x
Use the form of differential , hence :
begin{gathered} frac{dy}{dx} = frac{du}{dx} : . : v + u : . : frac{dv}{dx} \ frac{dy}{dx} = (4 {x}^{3} + 2)( {x}^{3} + 2 {x}^{2} + 1) + ( {x}^{4} + 2x)(3 {x}^{2} + 4x) \ frac{dy}{dx} = 4 {x}^{6} + 8 {x}^{5} + 4 {x}^{3} + 2 {x}^{3} + 4 {x}^{2} + 2 + 12 {x}^{6} + 4 {x}^{5} + 6 {x}^{3} + 8 {x}^{2} \ frac{dy}{dx} =16 {x}^{6} + 12 {x}^{5} + 12 {x}^{3} + 12 {x}^{2} + 2end{gathered}
dx
dy
=
dx
du
.v+u.
dx
dv
dx
dy
=(4x
3
+2)(x
3
+2x
2
+1)+(x
4
+2x)(3x
2
+4x)
dx
dy
=4x
6
+8x
5
+4x
3
+2x
3
+4x
2
+2+12x
6
+4x
5
+6x
3
+8x
2
dx
dy
=16x
6
+12x
5
+12x
3
+12x
2
+2