Constant rule and constant multiple rule Quiz 1

Question 1

Find $$y'$$, if $$y=21{{x}^{3}}+13x+9009$$.

Accepted Answer

$$63{{x}^{2}}+13$$

Answer

$$63{{x}^{2}}-13$$

Answer

$$63{{x}^{2}}+13x$$

Answer

$$63{{x}^{2}}-13x$$

Question 2

Find $$y'$$, if $$y=\sin ({{e}^{x}}+7)$$

Accepted Answer

$${{e}^{x}}\cos ({{e}^{x}}+7)$$

Answer

$$\cos x({{e}^{x}}+7)$$

Answer

$$\cos ({{e}^{x}}+7)$$

Answer

$$\cos ({{e}^{-x}}+7)$$

Question 3

Find $$y'$$, if $$y={{x}^{2}}\left( 7{{x}^{3}}+5 \right)\sqrt{\left( 7{{x}^{3}}+5 \right)}$$

Accepted Answer

$$x{{\left( 7{{x}^{3}}+5 \right)}^{\frac{1}{2}}}\left[ \dfrac{63}{2}{{x}^{3}}+2\left( 7{{x}^{3}}+5 \right) \right]$$

Answer

$$x{{\left( 7{{x}^{3}}+5 \right)}^{\frac{3}{2}}}\left[ \dfrac{63}{2}{{x}^{2}}+2\left( 7{{x}^{3}}+5 \right) \right]$$

Answer

$$x{{\left( 7{{x}^{3}}+5 \right)}^{\frac{1}{2}}}\left[ \dfrac{21}{2}x+2\left( 7{{x}^{3}}+5 \right) \right]$$

Answer

$$x{{\left( 7{{x}^{3}}+5 \right)}^{\frac{3}{2}}}\left[ \dfrac{3}{2}{{x}^{3}}+2\left( 7{{x}^{2}}+5 \right) \right]$$

Question 4

Find $$y'$$, if $$y=\sin \left( 2{{x}^{2}} \right)\cos \left( {{e}^{x}} \right)$$

Accepted Answer

$$-{{e}^{x}}\sin \left( 2{{x}^{2}} \right)\sin \left( {{e}^{x}} \right)+4x\cos \left( {{e}^{x}} \right)\cos \left( 2{{x}^{2}} \right)$$

Answer

$${{e}^{x}}\sin \left( 2{{x}^{2}} \right)\sin \left( {{e}^{x}} \right)-4x\cos \left( {{e}^{x}} \right)\cos \left( 2{{x}^{2}} \right)$$

Answer

$$-{{e}^{x}}\sin \left( 2{{x}^{2}} \right)\sin \left( {{e}^{x}} \right)+2x\cos \left( {{e}^{x}} \right)\cos \left( 2{{x}^{2}} \right)$$

Answer

$$-{{e}^{-x}}\sin \left( 2{{x}^{2}} \right)\sin \left( {{e}^{x}} \right)+4x\cos \left( {{e}^{x}} \right)\cos \left( 2{{x}^{2}} \right)$$

Question 5

Find $$yy'$$, if $$y=3\sqrt{4{{x}^{\frac{7}{2}}}+5{{x}^{\frac{3}{2}}}+\sqrt{2}x+8}$$

Accepted Answer

$$\dfrac{9}{4}\left( 28{{x}^{\frac{5}{2}}}+15{{x}^{\frac{1}{2}}}+2\sqrt{2} \right)$$

Answer

$$\dfrac{9}{2}\left( 28{{x}^{\frac{3}{2}}}+15{{x}^{\frac{1}{2}}}+2\sqrt{2} \right)$$

Answer

$$\dfrac{3}{4}\left( 28{{x}^{\frac{5}{2}}}+15{{x}^{\frac{1}{2}}}+2\sqrt{2} \right)$$

Answer

$$\dfrac{9}{2}\left( 28{{x}^{\frac{5}{2}}}+15{{x}^{\frac{1}{2}}}+2\sqrt{2} \right)$$