Question

calcule la derivada de la siguiente función aplicando las reglas de la derivación.
f(x)=(2x^2+3)^3 .(3x)^2x

Answer 1

Respuesta:

$3(2 {x}^{2} + 3)^{2} \times (4x) \times (3x)^{2x} + (2 {x}^{2} +3)^{3} \times \: ln(9) \times {9}^{x} \times {x}^{2x} + {9}^{x} \times {e}^{ln(x) \times 2x} \times ( \frac{1}{x} \times 2x + ln(x) \times 2)$

Explicación paso a paso:

$\frac{d}{dx} (( {2x}^{2} + 3)^{3} </p><p>\times (3x)^{2x} )$

$( \frac{d}{dx} (2 {x}^{2} + 3)^{3}) \times (3x)^{2x}+ (2 {x}^{2} + 3)^{3} \times( \frac{d}{dx} ( 3x)^{2x} )$

$3(2 {x}^{2} + 3)^{2} \times (\frac{d}{dx} (2 {x}^{2} + 3)) \times (3x)^{2x} + (2 {x}^{2} + 3)^{3} \times ( \frac{d}{dx} (3x)^{2x} )$

$3(2 {x}^{2} + 3)^{2} \times (4x) \times (3x)^{2x} + (2 {x}^{2} + 3)^{3} \times( \frac{d}{dx} ( {9}^{x} \times {x}^{2x} ))$

$3(2 {x}^{2} + 3)^{2} \times (4x) \times (3x)^{2x} + (2 {x}^{2} +3)^{3} \times ( \frac{d}{dx} (9^x)) \times {x}^{2x} + {9}^{x} \times ( \frac{d}{dx} (x^{2x} ))$

$3(2 {x}^{2} + 3)^{2} \times (4x) \times (3x)^{2x} + (2 {x}^{2} +3)^{3} \times \: ln(9) \times {9}^{x} \times {x}^{2x} + {9}^{x} \times {e}^{ln(x) \times 2x} \times ( \frac{1}{x} \times 2x + ln(x) \times 2)$