Differentiation of Trig. and exponential functions

Find the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)

Find the derivative of f(x) = 2e^2x + 3cosx.

• −3sin(x)

• 4e2x + 3sin(x)

• 4e2x

• 4e2x − 3sin(x)

The derivative of cos(2x²)

• -2xcos(2x²)

• -4xcos(2x²)

• -sin(2x²)

• -4xsin(2x²)

The derivative of xcos(2x²)

• cos(2x²) - 4x²sin(2x²)
• sin(2x²) - 4x²cos(2x²)
• cos(2x²) + 4x²sin(2x²)
• cos(2x²) - 2x²cos(2x²)

 $\frac{\text{d}}{\text{d}y}\left(e^{\left(2x+1\right)}\right)^2$  

•  $4e^{\left(4x+2\right)}$  

•  $\frac{4}{e^{\left(4x+2\right)}}$  

•  $e^{\left(4x+2\right)}\left(8x^2+2x\right)$  

•  $\frac{\left(8x^2+2x\right)}{e^{\left(4x+2\right)}}$  

 $\frac{\text{d}}{\text{d}y}\left(x^3-2xe^x\right)$  

•  $3x^2-2e^x\left(x+1\right)$  

•  $3x^2-2\left(e^x+\frac{x}{e^x}\right)$  

•  $3x^2-2xe^x\left(2x+1\right)$  

•  $3x^2-2x\left(2xe^x+\frac{1}{e^x}\right)$  

The derivative of sin(2x)

• 2cos(x)
• 2sin(2x)
• 2cos(2x)
• 2xcos(2x)

If  $y=e^{\sin x}$ , then  $\frac{dy}{dx}$ . 

•  $e^{\cos x}$  

•  $\cos x\cdot e^{\sin x}$  

•  $e^{\sin x}$  

•  $\ln\left(\sin x\right)\cdot e^{\sin x}$