Calculo

DETERMINA LA DERIVADA DE UNA FUNCION APLICANDO LAS FORMULAS FUNDAMENTALES.
1.- y = 2x - 7x^3 y= 2(1) – 7(3)x^(3-1) y= 2 - 21x^22.- y= 3x^2 + 5x – 1 dy/dx= 6x +5
3.- s = 2t^3 + 4t^2 – 3t ds/dx = 6t^2 8t – 3

4.- s =(t+1)/tds/dx (= t ds/dx t + 1 – t +1 ds/dx t)/〖(t)〗^2 dy/dx = (t(1)-(t+1)(1))/t^2 ds/dx = (t-t-1)/t^2 = (-1)/t^2

5.- y = 1/(√5x)1 (5x)^((-1)⁄2) dy/dx= 1dy/dx 5x^((-1)⁄2) = 1(5) ((-1)⁄2) x^(-1-1⁄2)= 1(5)-1⁄2 x^□((-3)⁄2)= -5⁄2 x^□((-3)/2)=(-5)/(2√(2&x^3 ))

6.- r = √t-5 (t -5)^(1⁄2) ½ (t-5)^((-1)⁄2) = 1/√(2&t-5)

7.- y = x(2 –x) 2x - x^2 = 2 – 2x

8.- y= x^3/(∛x^2 ) - 〖5x〗^2/√(5&x^4 ) + 8√(8&x^5 ) dy/dx= x^3 〖(x)〗^((-2)⁄3) = x^3 dy/dx= x^((-2)⁄3)+x^((-2)⁄5) dy/dx= x^3-2/5 x^((-7)⁄5) +x^((-2)⁄5) 3x^2=〖-2x〗^2/(5√(5&x^7 ))+ 〖3x〗^2/√(5&x^2 )〖dy/dx=-5x^2 X^((-4)⁄2)=5x^(2 dy/dx=) X^((-4)⁄2)+ X^((-4)⁄2) dy/dx 5x^2= -5x〗^2-4/2 X^(-3)+X^((-4)⁄2) (10x)=(20x^2)/(2x^3 )+10x/√(2&x^4 )dy/dx=8√(8&x^5 )=8 dy/dx X^(5⁄8)=8 5/(8 ) X^((-3)⁄8)= 40/8 X^((-3)⁄8)= 5/√(8&x^3 )

9.- u= 1/(x^2+9)1(x^2+〖9)〗^((-1)⁄2) = 1- 1⁄(2 )(x^2+9)^(-1-1⁄2)= -2x/(2√(2&〖(x〗^2+9)^3 ))


10.- t = ∛(x^2 ) +b^(2⁄3) dt/dx= 2/3 b^(-1+2⁄3) = 2/(3√(3&b))