Ayudenme porfavor son derivadas
1) d/dx (4+3×-2x³) = 3-6x²
2)d/dz (z²/z - z⁷/7 ) = z-z⁶
3) d/dx ( 2/x -3x(elevado a la x)) = -2/x²+6/x³
4)d/dx (2x¾ +4x-¼) =3/2 x-¼ -x-⁵/⁴
Respuestas a la pregunta
Las derivadas siguientes se comprueban a continuación :
1) d/dx ( 4 + 3x -2x³ ) = 3 - 6x²
d/dx ( 4 + 3x -2x³) = d(4)/dx + d(3x)/dx - d(2x³)/dx
= 0 + 3* dx/dx - 2*3* x²*dx/dx
= 3 * 1 - 6x²* 1
= 3 - 6x²
2) d/dz ( z²/2 - z⁷/7 ) = z - z⁶
d/dz( z²/2 - z⁷/7 ) = d(z²/2)/dz - d(z⁷/7)
= 1/2 *dz²/dz - 1/7 * dz⁷/dz
= 1/2* 2z dz/dz - 1/7 *7z⁶*dz/dz
= z - z⁶
3 ) d/dx ( 2/x - 3/x² ) = -2/x² + 6/x³
d/dx ( 2/x - 3/x² ) = d(2/x)/dx - d(3/x²)/dx
= 2 *d( x⁻¹)/dx - 3* d(x⁻²)/dx
= 2*-1 *x ⁻² dx/dx - 3* -2*x ⁻³ dx/dx
= -2/x² + 6/x³
4) d/dx (2x¾ +4x-¼) =3/2 x-¼ -x-⁵/⁴
d/dx (2x¾ +4x-¼) = d(2x³/₄ )dx + d(4x⁻¹/₄)/dx
= 2* d(x³/₄)/dx + 4*d(x⁻¹/₄)/dx
= 2* 3/4 * x^(³/₄ - 1 ) dx/dx + 4* -1/4 *x^(⁻¹/₄ -1)dx/dx
= 3/2x⁻¹/⁴ - x⁻⁵/⁴