Find the derivative of the function y=3x^2e^(2x)sin(x).

y is the product of three different function, so we would use the product rule in order to calculate the derivative of the curve. In order to apply the product rule we need to find the derivatives of each of the three functions separately. y1=3x2         -->      dy1/dx = 6x [by simply using the chain rule of differentiation] y2=e2x         -->      dy2/dy = 2e2x y3=sin(x)     -->      dy3/dx = cos(x) According to the product rule each function is to be differentiated one at a time and the other functions remain unchanged. Therefore the derivative of the function y=3x2e2xsin(x) is: dy/dx = 6xe2xsin(x) + 6x2e2xsin(x) + 3x2e2xcos(x).

SR
Answered by Shreya R. Maths tutor

6209 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Line AB, with equation: 3x + 2y - 1 = 0, intersects line CD, with equation 4x - 6y -10 = 0. Find the point, P, where the two lines intersect.


A function is defined by f(x)=x/(2x-2)^(1/2): (a)Determine the maximum domain of f. (b)Differentiate f. (c)Find the inflection points of the function's graph.


How would I go about drawing the graph of f(x) = sin(x)/(e^x) for -π≤x≤2π?


A mass of 3kg rests on a rough plane inclined at 60 degrees to the horizontal. The coefficient of friction is 1/5. Find the force P acting parallel to the plane applied to the mass, in order to just prevent motion down the plane.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning