Fórmula general
d(uⁿ) = nuⁿ⁻¹ du
d................dx
Ejemplos:
d((x²+1)⁷)
u=x²+1
du=2x
n=7
=7(x²+1)⁶(2x)
=14x(x²+1)⁶
d((3x+4)³)
dx
u=3x+4
du=3
n=3
=3(3x+4)²(3)
=9(3x+4)²
d((6x³+2x)⁴)
dx
u=6x³+2x
du=18x²+2
n=4
=4(6x³+2x)³(18x²+2)
=72x²+8(6x³+2x)³
d((3x+4x²)⁶)
dx
u=3x+4x²
du=3+8x
n=6
=6(3x+4x²)⁵(3+8x)
=48x+18(3x+4x²)⁵
d((7x⁴+3x³-6x)⁵)
dx
u=7x⁴+3x³-6x
du=28x³+9x²-6
n=5
du=18x²+2
n=4
=4(6x³+2x)³(18x²+2)
=72x²+8(6x³+2x)³
d((3x+4x²)⁶)
dx
u=3x+4x²
du=3+8x
n=6
=6(3x+4x²)⁵(3+8x)
=48x+18(3x+4x²)⁵
d((7x⁴+3x³-6x)⁵)
dx
u=7x⁴+3x³-6x
du=28x³+9x²-6
n=5
=5(7x⁴+3x³-6x)⁴(28x³+9x²-6)
=140x³+45x²-30(7x⁴+3x³-6x)⁴
Fórmula:
d (eᵘ)=eᵘdu
dx dx
d(e³ˣ)
dx
u=3x du=3
e³ˣ(3)
=3e³ˣ
Fórmula
d(Cosᵘ=-Sen(u)du
dx dx
d (Cos(2x⁴+4x))
dx
=-Sen(2x⁴+4x)8x³+4
=(-8x³-4)(Sen(2x+4x))
Fórmula:
d (eᵘ)=eᵘdu
dx dx
d(e³ˣ)
dx
u=3x du=3
e³ˣ(3)
=3e³ˣ
Fórmula
d(Cosᵘ=-Sen(u)du
dx dx
d (Cos(2x⁴+4x))
dx
=-Sen(2x⁴+4x)8x³+4
=(-8x³-4)(Sen(2x+4x))
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