Question: 4. Using the compound angle formula cos(A B] = cos A cos B + sin A sin B , nd the acute angle x such

4. Using the compound angle formula cos(A B] = cos A cos B + sin A sin B , nd the acute angle x such that 3x I ' 3x ' x 132 coscos+s1ns1n= 2 2 2 2 2 a) lim (x - 3x - 2x + 1 b) lim x + 2x c) lim . 4 d) lim x-0 x- - 2x x 7x+4 2. Find the derivatives of the following functions from first principles. a) f ( x) = 2x b) f ( x) = x + 2x -1 c) f (x) =x/2 3. Evaluate the first derivative of the following functions. a) f(x) = 6x + 3x -2x+99 b) y=(2x+3)(3x -1) c) y=x 2+2x+7x 4. Differentiate the following functions with respect to x. a) y= 2x+ cos(x) b) y = sin(2x) c ) f (x ) = (x+89 ) d) y = tan(x) ) f(x)=ex D f (x) = 2In(2x) 5. Find dy for each of the following functions. dx a) y= 3x +5x+7 b) y = 5 sin 2x 6. Given y = x + 2x. Calculate the rate of change of y when x is a) 6 b) - 5 c) 0

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