Differentiation rules Quiz 1

Question 1

Solve: $$\dfrac{d}{dx}\left( \dfrac{{{x}^{10}}}{{{x}^{5}}} \right)=?$$

Accepted Answer

$$5{{x}^{4}}$$

Answer

$$4{{x}^{3}}$$

Answer

$$5{{x}^{-4}}$$

Answer

$$\dfrac{1}{5}{{x}^{-4}}$$

Question 2

If $$f(x)=x$$ then $$f''(x)=?$$

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$2$$

Answer

$$x$$

Question 3

Find the Derivative of $$y = 122{{x}^{5}} +	ext{ }31{{x}^{4}} +	ext{ }76{{x}^{3}} + {{x}^{2}} -	ext{ 1}9x +	ext{ 6}6$$ with respect to $$x$$.

Accepted Answer

$$	ext{610} {{x}^{4}} +	ext{ 124} {{x}^{3}} +	ext{ }228 {{x}^{2}} +	ext{ }2x -	ext{ 19}$$

Answer

$$	ext{610} {{x}^{4}} +	ext{ 12} {{x}^{3}} +	ext{ }28 {{x}^{2}} +	ext{ }x -	ext{ 19}   $$

Answer

$$	ext{60} {{x}^{4}} +	ext{ 12} {{x}^{3}} +	ext{ }28 {{x}^{2}} +	ext{ }x -	ext{ 19} $$

Answer

$$	ext{60} x +	ext{ 12} {{x}^{{}}} +	ext{ }28 {{x}^{2}} +	ext{ }x -	ext{ 19}  $$

Question 4

Solve $$y =	ext{ }{{e}^{x}}ln	ext{ }(55{{x}^{3}} +{{x}^{2}})$$

Accepted Answer

$${{e}^{x}}{{\left( 55{{x}^{3}} +{{x}^{2}} ight)}^{-1}} \left( 165{{x}^{2}} +	ext{ }2x ight)	ext{ }+	ext{ }{{e}^{x}}ln	ext{ }\left( 55{{x}^{3}} +{{x}^{2}} ight)  $$

Answer

$${{e}^{x}}{{\left( 5{{x}^{3}} +{{x}^{2}} ight)}^{-1}} \left( 55{{x}^{2}} +	ext{ }2x ight)	ext{ }+	ext{ }\left( 55{{x}^{3}} +{{x}^{2}} ight) $$

Answer

$${{x}^{n-1}}$$

Answer

None of the above

Question 5

Find $$\dfrac{dy}{dx}$$if,$$y=\dfrac{{{x}^{2}}}{In(1-45{{x}^{2}})}$$

Accepted Answer

$$\dfrac{dy}{dx}=\dfrac{2xIn(1-45{{x}^{2}})-90{{x}^{3}}{{(1-45{{x}^{2}})}^{-1}}}{{{(In(1-45{{x}^{2}}))}^{2}}}$$

Answer

$$\dfrac{dy}{dx}=\dfrac{5{{x}^{2}}In(1-{{x}^{2}})-90{{x}^{3}}{{(1-45{{x}^{2}})}^{-1}}}{{{(In(1-45{{x}^{2}}))}^{2}}}$$

Answer

$$\dfrac{(1-{{x}^{2}}){{-}^{{}}}(1-45{{x}^{2}})}{{{(1-45{{x}^{2}})}^{{}}}}$$

Answer

None of the above