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The derivative and equation of the tangent line

Calculus
Tutor: None Selected Time limit: 1 Day

(2x 3sinPix)^4

Oct 22nd, 2014

Ok, so you have to use the power rule and the chain rule twice.

d/dx(2x3sinPix)^4 = 4(2x3sinPix)^3*[2x(3cosPix)(Pi) + (3sinPix)(2)]

= [4(8x^3(27)sin^3Pix][6PixcosPix = 6sinPix]

= 5184Pix^4sin^3PixcosPix + 5184x^3sin^4Pix

This derivative represent the SLOPE of any tangent line on the curve at any point on the curve.

Once you determine which point you want to use you then just plug in the x coordinate into the derivative to get a numerical value for the slope. Then you use the formula y = mx + b to determine the equation of the tangent line at that point.

Oct 23rd, 2014

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Oct 22nd, 2014
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