what is the Derivative of cos^3 (4theta +1) ?
So am doing this worksheet but cant do these questions always get to the same answer
a) cos^3 (4theta +1)
and
b) find y cord and gradient of tangent at the points on the curve corresponding to the given values of theta:
y=cos theta at theta = pi/4 and theta = pi/2
So am doing this worksheet but cant do these questions always get to the same answer
a) cos^3 (4theta +1)
and
b) find y cord and gradient of tangent at the points on the curve corresponding to the given values of theta:
y=cos theta at theta = pi/4 and theta = pi/2
1 Answer
Explanation:
#(a)#
#"differentiate using the "color(blue)"chain rule"#
#"given "y=f(g(x))" then"#
#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#
#"here "y=cos^3(4theta+1)=(cos(4theta+1))^3#
#rArrdy/(d theta)=3(cos(4theta+1))^2xxd/(d theta)(cos(4theta+1))#
#color(white)(rArrdy/(d theta))=3cos^2(4theta+1)xx-sin(4theta+1)xxd/(d theta)(4theta+1)#
#=-12cos^2(4theta+1)sin(4theta+1)#
#(b)#
#•color(white)(x)m_(color(red)"tangent")=dy/(d theta)" at x = a"#
#y=costhetarArrdy/(d theta)=-sintheta#
#•color(white)(x)x=pi/4rArry=cos(pi/4)=1/sqrt2=sqrt2/2#
#color(white)(x) " at "(pi/4,sqrt2/2)tody/(d theta)=-sin(pi/4)=-sqrt2/2#
#•color(white)(x)x=pi/2rArry=cos(pi/2)=0#
#color(white)(x) " at "(pi/2,0)tody/(d theta)=-sin(pi/2)=-1#