Question

hallar la derivada de la función (5x^2+7x)^3​

Answer 1

Explicación paso a paso:

Cambio de variable u

$u = (5 {x}^{2} + 7x) \\ d{u}^{3} = 3 {u}^{2}$

Regla de la cadena

$\frac{ {du}^{3} }{du} \times \frac{du}{dx} \\ 3 {u}^{2} \times du \\ 3( {5 {x}^{2} + 7x) }^{2} \times (10x + 7) \\ 3(25 {x}^{4} + 70 {x}^{3} + 49 {x}^{2} ) \times (10x + 7) \\ (75 {x}^{4} + 210 {x}^{3} + 147 {x}^{2}) \times (10x + 7) \\ 750 {x}^{5} + 2100 {x}^{4} + 1470 {x}^{3} + 525 {x}^{4 } + 1470 {x}^{3} + 1029 {x}^{2} \\ 750 {x}^{5} + 2625 {x}^{4} + 2940 {x}^{3} + 1029 {x}^{2}$