Question

Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of the tangent line to the curve given by X+ y^2 = 15 at the point (-1,4). Enter the slope as a number with one digit to the left of the decimal point and 3 digits to the right of the decimal point. For instance 1.234 or -1.234 or as a fraction.

Answer 1

Though we can answer one question at time but we have provided solutions to all 3 question.

Questions f(= cos (sin13x)) Need to 4ud de irrative of it- tix = elf a a (costsin (3x7) = siulsin (36)) .a (sin 34 ) da Apply chain Rule of differentiation = -sin lsink3n)) cay 3x (3x) - sinisin (381) .205 33.42(X) - Sin i sin 13x)) Cos3x 3.1 - 3 co zn sin (sin 3x) Ane Question 2: ifrw = cos (x2+2x) And derivative of fuko f'rxe) - fx = sta (cos (x²+2x)) - Sin( x + 2x) 3 (423) - sinfx2+2x) ((2x)) -- Sin (x² + 2x) (2x + 2.1) 5-(2x+2).5 9n (*? + 2%) As Question 3 slope of tauscut Curve: 7+4? = 15 e te * + y29 = US) => 1+2y-egy So dy de ma ży at (-1,4) dx