Trig differentiation

To differentiate

 $y=\sec^3x$  I should use

• Product rule

• Quotient rule

• Chain rule

 $\sin\left(x^2+1\right)$  differentiates to

•  $2x\sin\left(x^2+1\right)+\cos\left(x^2+1\right)$  

•  $2x\sin\left(x^2+1\right)$  

•  $2x\cos\left(x^2+1\right)$  

•  $\cos\left(x^2+1\right)+\sin\left(2x\right)$  

To show that

 $\tan\ x$  differentiates to  $\sec^2x$   I must use the

• Chain rule

• Product rule

• Quotient rule

 $y=\tan\left(3x\right)$  then  $\frac{dy}{dx}=$  

•  $3\sec\left(3x\right)$  

•  $\sec^2\left(3x\right)$  

•  $3x\sec^2\left(3x\right)$  

•  $3\sec^2\left(3x\right)$  

 $y=\operatorname{cosec}\left(10x+4\right)$  find  $\frac{dy}{dx}$  

•  $-10\operatorname{cosec}\left(10x+4\right)\cot\left(10x+4\right)$  

•  $10\operatorname{cosec}\left(10x+4\right)\cot\left(10x+4\right)$  

•  $-10\operatorname{cosec}\left(10x+4\right)$  

•  $10\operatorname{cosec}\left(10x+4\right)\cot\left(10x+4\right)$  

 $y=\frac{\tan x}{x}$  find  $\frac{dy}{dx}$  

•  $x\sec^2x-\tan x$  

•  $x\sec^2x+\tan x$  

•  $\frac{x\sec^2x-\tan x}{x^2}$  

•  $\frac{\sec^2x}{1}$  

Differentiate $e^x\cot x$  

•  $-e^x\operatorname{cosec}^2x$  

•  $e^x\left(\cot x-\operatorname{cosec}^2x\right)$  

•  $xe^x\cot x-e^x\operatorname{cosec}^2x$  

•  $e^x\cot x-\operatorname{cosec}^2x$  

Differentiate $\tan e^x$  

•  $e^x\tan x+e^x\sec^2x$  

•  $e^x\tan e^x+e^x\sec^2e^x$  

•  $e^x\tan x-e^x\sec^2x$  

•  $e^x\sec^2e^x$  

Differentiate $\frac{x}{\sec x}$  

•  $\frac{1}{\sec x\tan x}$  

•  $\cos x-x\sin x$  

•  $\frac{\sec x+x\sec x\tan x}{\sec^2x}$  

•  $\frac{\sec x-x\tan x}{\sec^2x}$