How do you solve these questions. As i keep getting them wrong (1 Viewer)

cossine

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Theorems
sin x(d/dx)= cos x

cos x(d/dx) = -sin x

-sin x(d/dx) = -cos x

-cos x(d/dx) = sin x

The proof of these theorems is outside the scope of high school however nothing will stop you from applying the theorem.

Other than that question are fairly straightforward, so you may need to apply product rule or chain rule
 

cossine

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Just remember these:

y = sin [ f(x) ]
y' = f'(x) x cos [ f(x) ]

y = cos [ f(x) ]
y' = f'(x) x -sin [ f(x) ]

y = tan [ f(x) ]
y' = f'(x) x sec^2 [ f(x) ]

Let's apply this to the question above:

y = sin [ 1/4x + pi/2 ]

So f(x) = 1/4x + pi/2

f'(x) = 1/4

Therefore y' = 1/4 x cos [ 1/4x + pi/2 ]

But the question is asking for y'(pi)

So in place of x, we now substitute x = pi

Doing this we get y'(pi) = 1/4 x cos [ 1/4(pi) + pi/2 ] = ________

You can take it step by step until you reach your answer, don't get overwhelmed :)
You could do this but it does not demonstrate understanding of chain rule.

As a side note you should use * for multiplication has "x" can be confused with the variable "x".
 

tywebb

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So this is year 12 Cambridge Advanced 6B Q1u, 4d, 5d, 12a
1u.png
It does seem that the answer in the textbook for this one is wrong. Textbook answer is but it should be
4.png
4d.png
5.png
5d.png
12a.png
 

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