2. (a) In each of the following, find y' and y". i. tan xy = y ii. sec² y + cot² y = 3 (b) If the curve sin y = x³-5 passes through the point (1,0), find y' and y" at (1,0). (c) In each of the following, find d i. y = ln (²1) (d) Find d if 3.x² i. y = coth 4r ii. y = sinh 2x cos x iii. tan² (y + 1) = 3 sinx. ii. y = iii. y = T2-1 sin r (2x+3) ª (log₂ x)

2) a) i) tan xy=y Differentiate both sides of the equation.

Resuelto 2. (a) In each of the following, find y' and y". i.

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Pregunta: 2. (a) In each of the following, find y' and y". i. tan xy = y ii. sec² y + cot² y = 3 (b) If the curve sin y = x³-5 passes through the point (1,0), find y' and y" at (1,0). (c) In each of the following, find d i. y = ln (²1) (d) Find d if 3.x² i. y = coth 4r ii. y = sinh 2x cos x iii. tan² (y + 1) = 3 sinx. ii. y = iii. y = T2-1 sin r (2x+3) ª (log₂ x)
2. (a) In each of the following, find y' and y". i. tan xy = y ii. sec² y + cot² y = 3 (b) If the curve sin y = x³-5 passes through the point (1,0), find y' and y" at (1,0). (c) In each of the following, find d i. y = ln (²1) (d) Find d if 3.x² i. y = coth 4r ii. y = sinh 2x cos x iii. tan² (y + 1) = 3 sinx. ii. y = iii. y = T2-1 sin r (2x+3) ª (log₂ x) (ln(sec.x)) T iii. y = tan=¹ (₁) iv. y = 2x sin 3x iv. tan(e-¹) = x² v. y = 3sin r v. y = cosh-¹(sin x)

Muestra el texto de la transcripción de la imagen
Hay 4 pasos para resolver este problema.
Solución
Paso 1
2) a)
i) $\tan x y = y$
Differentiate both sides of the equation.
Mira la respuesta completa
Paso 2
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Paso 3
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Paso 4
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Respuesta
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Texto de la transcripción de la imagen:

2. (a) In each of the following, find

y^{'}

and

y^{''}

. i.

tan x y = y

iii.

tan^{2} (y + 1) = 3 sin x

. ii.

sec^{2} y + cot^{2} y = 3

(b) If the curve

sin y = x^{3} - x^{5}

passes through the point

(1, 0)

, find

y^{'}

and

y^{''}

(1, 0)

. (c) In each of the following, find

\frac{d y}{d x}

. i.

y = ln (\frac{x - 1}{x + 1})

ii.

y = \frac{x ^{2} - 1 sin x}{( 2 r + 3 ) ^{4}}

iv.

tan (e^{y^{- x}}) = x^{2}

iii.

y = (lo g_{2} x) (ln (sec x))

y = 3^{s i n x}

(d) Find

\frac{d y}{d x}

if i.

y = \frac{3 s ^{2}}{cth 4 x}

iii.

y = tan^{- 1} (\frac{x}{1 - x ^{2}})

y = cosh^{- 1} (sin x)

ii.

y = sinh 2 x cos x

iv.

y = 2 x sin^{- 1} 3 x