Fundamentals of Differentiation

$3x^2 + 2$

$3x + 2$

$6x + 2$

$6x^2 + 2x$

Undefined

$\frac{-1}{ \left|x\right|^2 }$

$\frac{-1}{ \left|x\right| }$

$\frac{-1}{ \left|x\right|^3 }$

$(x^2)(e^x) + (e^x)(2x)$

$(e^x)(e^x) + (2)(e^x)$

$(2)(e^{(x)}) + (e^{(}))$

$(0) + (0)$

5

-3

3

8

$\phi '(u(x))=\sin(5)(x)(\cos(x))$

$\phi '(u(x))=5\sin^{4}(x)\cos(x)$

$\phi '(u(x))=5\sin^{5}(x)$

$\phi '(u(x))=\cos(x)(\sin(5)(x))$

$12x^3 - 4x^2$

$12x^3 - 2x^2$

$12x^2 - 2x$

$12x^2 - 4x$

$2x + 3$

$6x + 3$

$6x$

$3x + 1$

Quotient Rule because it directly applies to ratios of functions

Chain Rule thinking that one function is composed within another

Product Rule treating $\ln(t)$ and $t^{-3}$ as separate factors

Logarithmic Differentiation since there's a natural logarithm present

Incorrectly constructed questions

Incorrectly constructed question

Incorrectly constructed questions

Cos[u]-Cos[x]

12

$3x - 2$

4

3