Trigonometric derivatives Quiz 1

Question 1

Find the derivative of the function $$\dfrac{1}{2\sinh -4\cosh }$$ w.r.t $$''h''$$.

Accepted Answer

$$\dfrac{-2\cosh -4\sinh }{{{\left( 2\sinh -4\cosh  \right)}^{2}}}$$

Answer

$$\dfrac{2\cosh +4\sinh }{{{\left( 2\sinh -4\cosh  \right)}^{2}}}$$

Answer

$$\dfrac{-2\sinh -4\cosh }{{{\left( 2\sinh -4\cosh  \right)}^{2}}}$$

Answer

$$\dfrac{2\sinh +4\cosh }{{{\left( 2\sinh -4\cosh  \right)}^{2}}}$$

Question 2

Find $$f'\left( v ight)$$ for $${{v}^{3}}	an v$$  at $$v=\dfrac{\pi }{4}$$.

Accepted Answer

$$\dfrac{{{\pi }^{2}}}{16}\left( \dfrac{\pi }{2}+3 \right)$$

Answer

$$\dfrac{{{\pi }^{2}}}{16}\left( \dfrac{\pi }{2}+2 \right)$$

Answer

$$\dfrac{{{\pi }^{2}}}{16}\left( \dfrac{\pi }{2}-3 \right)$$

Answer

$$\dfrac{{{\pi }^{2}}}{16}\left( \dfrac{\pi }{2}-2 \right)$$

Question 3

If $$f\left( x ight)=	an x+9\cos x$$  is the given curve then find the equation of the tangent for the curve at $$x=\pi $$.

Accepted Answer

$$y=x-\pi -9$$

Answer

$$y=x+\pi +9$$

Answer

$$y=x+\pi -9$$

Answer

$$y=-x-\pi -9$$

Question 4

Find the value of $$f'\left( \dfrac{\pi }{4} ight)$$, if $$f\left( \beta ight)=	an \beta \sec \beta $$.

Accepted Answer

$$3\sqrt{2}$$

Answer

$$4$$

Answer

$$2\sqrt{2}$$

Answer

$$2$$

Question 5

Find the equation of a line which is perpendicular to the curve  $$y=\dfrac{	an x}{1+	an x}$$ at $$x=\dfrac{\pi }{4}$$

Accepted Answer

$$y=-2x+\dfrac{\pi +1}{2}$$

Answer

$$y=-x+\dfrac{\pi +1}{4}$$

Answer

$$y=-2x-\dfrac{\pi +1}{2}$$

Answer

$$y=2x+\dfrac{\pi +1}{2}$$