Let f(x) = 5x^4 + 6x^3 + 3, find dy/dx at x = 3
First we must differentiate the equation with respect to x. To differentiate you must multiply the coefficient (number in front) by the power of x, then subtract 1 from the power. So here we find dy/dx = (54)x^(4-1) + (63)x^(3-1) + (1*0) = 20x^3 + 18x^2.
To find the value of dy/dx at x=3 we must substitute x=3 into the equation we just found. This gives dy/dx = (203^3) + (183^2) = 540 + 162 = 702. This value is the gradient of the line at x=3.
FK
Related Maths A Level answers
All answers ▸Given that y = 5x^2 - 4/(x^3), x not equal to 0, find dy/dx.
Why do we have to use radians instead of degrees?
Find the equation of the line tangential to the function f(x) = x^2+ 1/ (x+3) + 1/(x^4) at x =2
Having a rectangular parking lot with an area of 5,000 square yards that is to be fenced off on the three sides not adjacent to the highway, what is the least amount of fencing that will be needed to complete the job?