Find dy/dx when y = 5x^6 + 4x*sin(x^2)

Looking at the first element of the equation 5x6, we can simply multiply 6 by 5 to give 30 and subtract 1 from the power of x. So d/dx[5x6] = 30x5. The next element of the equation is 4xsin(x2), where we will need to use the product rule (since we have the variable x in both 4x and sin(x2) which are being multiplied) and chain rule (for sin(x2) since this is the composition of the two functions sin() and x2). From the product rule we obtain 4sin(x2) + 4xd/dx[sin(x2)]. Using the chain rule to differentiate sin(x2), we get cos(x2)d/dx[x2] = 2xcos(x2). Therefore our end result for dy/dx = 30x5 + 4sin(x2) + 4x2xcos(x2) = 30x5 + 4*sin(x2) + 8x2*cos(x2)

Answered by Mark J. Maths tutor

2654 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

At each point P of a curve for which x > 0 the tangent cuts the y-axis at T, and N is the foot of the perpendicular from P to the y-axis. If T is always 1 unit below N and the curve passes through the point (1,0), find the Cartesian equation of the curve.


Given that y= 5x^2 + 2x , find dy/dx


What are the uses of derivatives in algebra?


What is the magnitude and direction of the resultant force of 3N horizontal and 5N vertical?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences