In Problems 1−8, find d3y/dx3. 1. y=x3+3x2+6x 2. y=x5+x4 3. y=(3x+5)3 4. y=(3−5x)5 5. y=sin(7x) 6. y=sin(x3) 7. y=x−11 8. y=1−x3x In Problems 9-16, find f′′(2). 9. f(x)=x2+1 10. f(x)=5x3+2x2+x 11. f(t)=t2 12. f(u)=5−u2u2 13. f(θ)=(cosθπ)−2 14. f(t)=tsin(π/t) 15. f(s)=s(1−s2)3 16. f(x)=x−1(x+1)2

1) Given that y=x^3+3x^2+6x First we have to find dy/dx Differentiate both sides with respect to x.

Resuelto In Problems 1−8, find d3y/dx3. 1. y=x3+3x2+6x 2.

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Pregunta: In Problems 1−8, find d3y/dx3. 1. y=x3+3x2+6x 2. y=x5+x4 3. y=(3x+5)3 4. y=(3−5x)5 5. y=sin(7x) 6. y=sin(x3) 7. y=x−11 8. y=1−x3x In Problems 9-16, find f′′(2). 9. f(x)=x2+1 10. f(x)=5x3+2x2+x 11. f(t)=t2 12. f(u)=5−u2u2 13. f(θ)=(cosθπ)−2 14. f(t)=tsin(π/t) 15. f(s)=s(1−s2)3 16. f(x)=x−1(x+1)2
Muestra el texto de la transcripción de la imagen
Hay 3 pasos para resolver este problema.
Solución
Paso 1
1) Given that $y = x^{3} + 3 x^{2} + 6 x$
First we have to find $\frac{d y}{d x}$
Differentiate both sides with respect to x.
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Paso 2
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Paso 3
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Respuesta
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Texto de la transcripción de la imagen:

In Problems

1 - 8

, find

d^{3} y / d x^{3}

. 1.

y = x^{3} + 3 x^{2} + 6 x

y = x^{5} + x^{4}

y = (3 x + 5)^{3}

y = (3 - 5 x)^{5}

y = sin (7 x)

y = sin (x^{3})

y = \frac{1}{x - 1}

y = \frac{3 x}{1 - x}

In Problems 9-16, find

f^{''} (2)

. 9.

f (x) = x^{2} + 1

10.

f (x) = 5 x^{3} + 2 x^{2} + x

11.

f (t) = \frac{2}{t}

12.

f (u) = \frac{2 u ^{2}}{5 - u}

13.

f (θ) = (cos θ π)^{- 2}

14.

f (t) = t sin (π / t)

15.

f (s) = s (1 - s^{2})^{3}

16.

f (x) = \frac{( x + 1 ) ^{2}}{x - 1}