Implicit derivative: Find dy/dx

label Calculus
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y= [(x^4 + 3) / cos (x) ] ^3

May 15th, 2015

y= [(x^4 + 3) / cos (x) ] ^3 =(x^4 + 3)^3 / [cos (x) ] ^3

dy/dx= [ 3(x^4 + 3)^2 * 4x^3 * [cos (x) ] ^3 - 3(x^4 + 3)^3 * [cos(x)]^2 * (-sin(x)) ] / [cos (x) ] ^6 =

= 12x^3 * (x^4 + 3)^2 *(1/[cos (x) ] ^3) + 3 (x^4 + 3)^3 * sin(x) * (1/ [cos (x) ] ^4) =

= 12x^3 * (x^4 + 3)^2 * [sec (x)]^3 + 3 (x^4 + 3)^3 * tan(x) * [sec (x)]^3

May 15th, 2015

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May 15th, 2015
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