If y - 4 log2cos ecx - 9 log3x then show that dydx - 0

We know that a^log x=x^log a . Now y=4^log_2(cosec x) 9^log_3 x=(cosec x)^log_24 ( x)^log_39= (cosec x)^2 ( x)^2 Hence, dydx=2(cosec x)( cosec x x) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Equations

If y = 4 lo...

Question

If $y = {(4)}^{{log}_{2} cos e c x} - {(9)}^{{log}_{3} cot x}$ then show that $\frac{d y}{d x} = 0$

Open in App

Solution

We know that $a^{log x} = x^{log a}$ . Now

$y = 4^{{log}_{2} (c o s e c x)} - 9^{{log}_{3} cot x} = (c o s e c x)^{{log}_{2} 4} - (cot x)^{{log}_{3} 9} = (c o s e c x)^{2} - (cot x)^{2}$

Hence,

$\frac{d y}{d x} = 2 (c o s e c x) (- c o s e c x cot x) - 2 cot x (- c o s e c x cot x) = 0$

Suggest Corrections

Similar questions

Q. If

\sqrt{x} + \sqrt{y} = 10

then show that

\frac{d x}{d y} + \sqrt{\frac{y}{x}} = 0

If $y = 3 cos (log x) + 4 sin (log x)$ , then show that $x^{2} \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} + y = 0$

Q. If

x

and

y

are differentiable functions of

t

, then show that

\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}}

\frac{d x}{d t} \neq 0

Q. If

x \sqrt{1 + y} + y \sqrt{1 + x} = 0

, then show that

\frac{d y}{d x} = - \frac{1}{(1 + x)^{2}}

Q. If

y = a e^{2 x} + b e^{- x}

, then show that

\frac{d^{2} y}{d x^{2}} - \frac{d y}{d x} - 2 y = 0

Join BYJU'S Learning Program

If y=(4)log2cosecx−(9)log3cotx then show that dydx=0

We know that alogx=xloga. Nowy=4log2(cosec x)−9log3cotx=(cosec x)log24−(cotx)log39=(cosec x)2−(cotx)2Hence,dydx=2(cosec x)(−cosec xcotx)−2cotx(−cosec xcotx)=0

If $y = {(4)}^{{log}_{2} cos e c x} - {(9)}^{{log}_{3} cot x}$ then show that $\frac{d y}{d x} = 0$

We know that $a^{log x} = x^{log a}$ . Now

$y = 4^{{log}_{2} (c o s e c x)} - 9^{{log}_{3} cot x} = (c o s e c x)^{{log}_{2} 4} - (cot x)^{{log}_{3} 9} = (c o s e c x)^{2} - (cot x)^{2}$

Hence,

$\frac{d y}{d x} = 2 (c o s e c x) (- c o s e c x cot x) - 2 cot x (- c o s e c x cot x) = 0$