Math  /  Calculus

QuestionWhat is the first derivative of t(x)=ln(4x3+4x2+6x+4)t(x)=\ln \left(4 x^{3}+4 x^{2}+6 x+4\right) ?
Select the correct answer below: 14x3+4x2+6x+4\frac{1}{4 x^{3}+4 x^{2}+6 x+4} 12x2+8x+64x3+4x2+6x+4\frac{12 x^{2}+8 x+6}{4 x^{3}+4 x^{2}+6 x+4} 12x2+8x+6ln(4x3+4x2+6x+4)\frac{12 x^{2}+8 x+6}{\ln \left(4 x^{3}+4 x^{2}+6 x+4\right)} ln(12x2+8x+6)\ln \left(12 x^{2}+8 x+6\right) 4x3+4x2+6x+412x2+8x+6\frac{4 x^{3}+4 x^{2}+6 x+4}{12 x^{2}+8 x+6}

Studdy Solution
Apply the chain rule to find t(x) t'(x) :
t(x)=u(x)u(x)=12x2+8x+64x3+4x2+6x+4 t'(x) = \frac{u'(x)}{u(x)} = \frac{12x^2 + 8x + 6}{4x^3 + 4x^2 + 6x + 4}
The correct answer is:
12x2+8x+64x3+4x2+6x+4 \boxed{\frac{12x^2 + 8x + 6}{4x^3 + 4x^2 + 6x + 4}}

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