1. Find the derivatives of the following functions. (a) f(x)=e7x3+2x (f) f(x)=x2−57e5x (b) y=(3x)2 (c) y=3x2 (g) y=3ln(x)+2ln(3x+2) (d) f(x)=eπ (e) f(x)=ex3+11 (h) y=x2+(x+x3+(x+x2)3)2

Finding derivatives of following functions: (a) Hence required answer is (21x^2+2)e^(7x^3+2x) .

Resuelto 1. Find the derivatives of the following functions.

Nuestra ayuda de expertos desglosó tu problema en una solución confiable y fácil de entender.

Pregunta: 1. Find the derivatives of the following functions. (a) f(x)=e7x3+2x (f) f(x)=x2−57e5x (b) y=(3x)2 (c) y=3x2 (g) y=3ln(x)+2ln(3x+2) (d) f(x)=eπ (e) f(x)=ex3+11 (h) y=x2+(x+x3+(x+x2)3)2

Muestra el texto de la transcripción de la imagen
Hay 4 pasos para resolver este problema.
Solución
Paso 1
Finding derivatives of following functions:

$(a)$
$\begin{matrix} \begin{aligned} \frac{d f (x)}{d x} & = \frac{d e^{7 x^{3} + 2 x}}{d x} \\ f^{'} (x) & = e^{7 x^{3} + 2 x} \times (7 \frac{{d x}^{3}}{d x} + 2 \frac{d x}{d x}) \\ = e^{7 x^{3} + 2 x} \times (7 \times 3 x^{2} + 2) \\ = (21 x^{2} + 2) e^{7 x^{3} + 2 x} \end{aligned} \end{matrix}$
Hence required answer is $(21 x^{2} + 2) e^{7 x^{3} + 2 x}$ .
Mira la respuesta completa
Paso 2
Desbloquea
Paso 3
Desbloquea
Paso 4
Desbloquea
Respuesta
Desbloquea

Texto de la transcripción de la imagen:

1. Find the derivatives of the following functions. (a)

f (x) = e^{7 x^{3} + 2 x}

(f)

f (x) = \frac{7 e ^{5 x}}{x ^{2} - 5}

(b)

y = (3^{x})^{2}

(c)

y = 3^{x^{2}}

(g)

y = \frac{l n ( 3 x + 2 )}{3 l n ( x ) + 2}

(d)

f (x) = e^{π}

(e)

f (x) = \frac{1}{e ^{x^{3}} + 1}

(h)

y = x^{2} + (x + x^{3} + (x + x^{2})^{3})^{2}