Find the derivative of 2x⁴ + x

1

(a)

8x³+1

Find the derivative of the following functions.
\(\frac { 3x+4 }{ 5x^{ 2 }-7x+9 } \)

1

(a)

\(y=\frac { 3x+4 }{ 5{ x }^{ 2 }-7x+9 }\)
\( \frac { dy }{ dx } =\frac { (5{ x }^{ 2 }-7x+9)\frac { d }{ dx } (3x+4)-(3x+4)\frac { d }{ dx } (5{ x }^{ 2 }-7x+9) }{ (5{ x }^{ 2 }-7x+9)^{ 2 } } \)
Ans: \(\frac { 55-15x^{ 2 }-40x }{ (5{ x }^{ 2 }-7x+9)^{ 2 } } \)

 

Find the derivative of the following functions.
cosecx cotx

1

(a)

-cosec³x-cot²x cosecx

Find the derivative of the following functions.
(secx-1)(secx+1)

1

(a)

(secx-1)(secx+1)=sec²x-1=tan²x
=tan x. tan x
Ans. 2tan x sec² x

Find the derivative of the following functions.
(ax²+cotx)(p+qcosx)

1

(a)

Let y = (ax² + cot x) (p + q cosx).
Then, \(\frac { dy }{ dx } =\left( { ax }^{ 2 }+cotx \right) \frac { d }{ dx } (p+qcosx)+(p+qcosx)\frac { d }{ dx } ({ ax }^{ 2 }+cotx)\)
\(=-qsinx({ ax }^{ 2 }+cotx)+(p+qcosx)(2ax-{ cosec }^{ 2 }x)\)