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i don't really have time to write out all my awnsers, but would appreciate if someone could give me the awnsers to these questions

i'm confident in my maths but just need someone to give me a rundown of the awnsers, because the book I'm using dosen't have any!

there are 12 questions in all, and most are REALLY easy and i really want to know if i got them right or not

differentiate:

1: f(x) = x sin x

differentiate

2: y = (1 + sin x) / (x + cos x)

find an equation of the tangent line to the curve at the given point

3: y = (1+ x) cos x, (0,1)

identify the inner function, outer function and find the derivative dy/dx

4: Squareroot(4+3x)

differentiate

5: f(x) = (x^2 - x +1)^3

differentiate

6: y=(a^3) + ((cos^3)*x)

find an equation of the tangent line to the curve at the given point

7: y = squareroot(5+x^2), (2,3)

find y by implicit differentiation

8: (4x^2 )+ (9y^2) = 36

then solve the equation explicityly for y and differentiate to get y' in terms of x

9:

10:

then check your solutions for 8:/9: are consisteny by substituting the expression for y into your solution for 8:

(n.b this is the one i had trouble with, 8,9,10)

find dy/dx by implicit differentiation

11: x^2 - 2xy + y^4 = c

(took me 10 minutes lol)

use implicit differentiation to find an equation tangent to the line of the curve to the point

12: x^2 + 2xy - y^2 + x =2

i'm confident in my maths but just need someone to give me a rundown of the awnsers, because the book I'm using dosen't have any!

there are 12 questions in all, and most are REALLY easy and i really want to know if i got them right or not

differentiate:

1: f(x) = x sin x

differentiate

2: y = (1 + sin x) / (x + cos x)

find an equation of the tangent line to the curve at the given point

3: y = (1+ x) cos x, (0,1)

identify the inner function, outer function and find the derivative dy/dx

4: Squareroot(4+3x)

differentiate

5: f(x) = (x^2 - x +1)^3

differentiate

6: y=(a^3) + ((cos^3)*x)

find an equation of the tangent line to the curve at the given point

7: y = squareroot(5+x^2), (2,3)

find y by implicit differentiation

8: (4x^2 )+ (9y^2) = 36

then solve the equation explicityly for y and differentiate to get y' in terms of x

9:

10:

then check your solutions for 8:/9: are consisteny by substituting the expression for y into your solution for 8:

(n.b this is the one i had trouble with, 8,9,10)

find dy/dx by implicit differentiation

11: x^2 - 2xy + y^4 = c

(took me 10 minutes lol)

use implicit differentiation to find an equation tangent to the line of the curve to the point

12: x^2 + 2xy - y^2 + x =2

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