Find the derivative of e 1 + 4 x </mrow>

Landon Mckinney

Landon Mckinney

Answered question

2022-04-10

Find the derivative of e 1 + 4 x 4 + 6 x 3 .

Answer & Explanation

kazneni3tr2b

kazneni3tr2b

Beginner2022-04-11Added 17 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)=e1+4x and g(x)=4+6x3.

(4+6x3)ddx[e1+4x]-e1+4xddx[4+6x3](4+6x3)2

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)=1+4x.

(4+6x3)(e1+4xddx[1+4x])-e1+4xddx[4+6x3](4+6x3)2

Differentiate.

4(4+6x3)e1+4x-18e1+4xx2(4+6x3)2

Simplify.

e1+4x(12x3-9x2+8)2(3x3+2)2

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