Quotient rule Quiz 1

Question 1

Value of derivative of $$f\left( x \right)=\dfrac{{{\sin }^{2}}x}{\cos x}$$ is

Accepted Answer

$$\dfrac{\sin 2x\left( \cos x \right)+{{\sin }^{3}}x}{{{\cos }^{2}}x}$$

Answer

$$\dfrac{\cos 2x\left( \cos x \right)-{{\sin }^{3}}x}{{{\cos }^{2}}x}$$

Answer

$$\dfrac{\cos 2x\left( \cos x \right)+{{\sin }^{3}}x}{{{\cos }^{2}}x}$$

Answer

$$\dfrac{\sin 2x\left( \cos x \right)-{{\sin }^{3}}x}{{{\cos }^{2}}x}$$

Question 2

Value of derivative of $$f\left( x \right)=\dfrac{{{x}^{3}}}{{{x}^{2}}+1}$$ is

Accepted Answer

$$\dfrac{{{x}^{2}}\left( {{x}^{2}}+3 \right)}{{{\left( {{x}^{2}}+1 \right)}^{2}}}$$

Answer

$$\dfrac{{{x}^{2}}\left( {{x}^{2}}+3 \right)}{{{\left( {{x}^{2}}-1 \right)}^{2}}}$$

Answer

$$\dfrac{{{x}^{2}}\left( {{x}^{2}}-3 \right)}{{{\left( {{x}^{2}}-1 \right)}^{2}}}$$

Answer

$$\dfrac{{{x}^{2}}\left( {{x}^{2}}-3 \right)}{{{\left( {{x}^{2}}+1 \right)}^{2}}}$$

Question 3

Value of derivative of $$f\left( x \right)=\dfrac{\sin x}{\cos x}$$ is

Accepted Answer

$${{\sec }^{2}}x$$

Answer

$$-	ext{cosec}^{2}x$$

Answer

$$	ext{cosec}^{2}x$$

Answer

$$-{{\sec }^{2}}x$$

Question 4

Value of derivative of $$f\left( x \right)=\dfrac{{{e}^{x}}}{{{x}^{2}}}$$ is

Accepted Answer

$$\dfrac{{{e}^{x}}\left( x-2 \right)}{x^3}$$

Answer

$$\dfrac{{{e}^{x}}\left( {{x}^{2}}-2 \right)}{{{x}^{2}}}$$

Answer

$$\dfrac{{{e}^{x}}\left( {{x}^{2}}+2 \right)}{{{x}^{2}}}$$

Answer

$$\dfrac{{{e}^{x}}\left( x+2 \right)}{x}$$

Question 5

Value of $$f'\left( y \right)$$ if $$f\left( y \right)$$$$=\dfrac{{{e}^{2{{y}^{2}}+5}}}{{{y}^{4}}}$$

Accepted Answer

$$\dfrac{{{e}^{2{{y}^{2}}+5}}.4{{y}^{3}}\left( {{y}^{2}}-1 \right)}{{{y}^{8}}}$$

Answer

$$\dfrac{{{e}^{2{{x}^{2}}+5}}.4{{x}^{3}}\left( {{x}^{2}}-1 \right)}{{{x}^{8}}}$$

Answer

$$\dfrac{{{e}^{2{{x}^{2}}+5}}.4{{x}^{3}}\left( {{x}^{2}}+1 \right)}{{{x}^{8}}}$$

Answer

$$\dfrac{{{e}^{2{{y}^{2}}+5}}.4{{y}^{3}}\left( {{y}^{2}}+1 \right)}{{{y}^{8}}}$$