Find the derivative of <mrow> 2 + 3 x + x

ureji1c8r1

ureji1c8r1

Answered question

2022-05-13

Find the derivative of 2 + 3 x + x 2 + 4 x 3 + 2 x 4 e 6 + 2 x  .

Answer & Explanation

Lankenp19hh

Lankenp19hh

Beginner2022-05-14Added 11 answers

Differentiate using the Quotient Rule which states that ddx[f(x)g(x)] is g(x)ddx[f(x)]-f(x)ddx[g(x)]g(x)2 where f(x)=2+3x+x2+4x3+2x4 and g(x)=e6+2x.

e6+2xddx[2+3x+x2+4x3+2x4]-(2+3x+x2+4x3+2x4)ddx[e6+2x](e6+2x)2

Differentiate.

e6+2x(3+2x+12x2+8x3)-(2+3x+x2+4x3+2x4)ddx[e6+2x]e12+4x

Differentiate using the chain rule, which states that ddx[f(g(x))] is f(g(x))g(x) where f(x)=ex and g(x)=6+2x.

e6+2x(3+2x+12x2+8x3)-(2+3x+x2+4x3+2x4)(e6+2xddx[6+2x])e12+4x

Differentiate.

e6+2x(3+2x+12x2+8x3)-2(2+3x+x2+4x3+2x4)e6+2xe12+4x

Simplify.

-4xe2x+6-10x2e2x+6+4x4e6+2x+e6+2xe12+4x

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