Aku & Maths: Takkan Terpisah (LEVEL 5)

Calculate the gradient of f(x)=ln(x)+x at x=2/3

• 0.261

• 2.5

• 1.5

• -0.405

What rule best apply to find the derivative of y=x lnx

• product rule

• quotient rule

• power rule

• sum rule

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)

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

•  $3x^2-2e^x\left(x+1\right)$  

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

•  $3x^2-2xe^x\left(2x+1\right)$  

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

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

•  $4e^{\left(4x+2\right)}$  

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

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

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

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

•  $3\left(e^x+2\right)\left(e^x+2x\right)^2$  

•  $3\left(e^x+2\right)^2$  

•  $3\left(e^x+4x^2\right)\left(e^x+2x\right)^2$  

•  $4\left(e^x+2\right)^4$  

Differentiate y = ln (5x - 7)

• _ 5 _

  5x-7

• _ 1 _

  5x-7

• ln5

• ln5x - ln 7

Find $\ \frac{\text{d}}{\text{d}x}\left[\ln\left(\frac{4x^2}{\left(3x-1\right)^2}\right)\right].$  

•  $\frac{2}{x}-\frac{6}{3x-1}$  

•  $\frac{4}{x}-\frac{2}{3x-1}$  

•  $\frac{x}{2}-\frac{3}{3x-1}$  

•  $\frac{x}{4}-\frac{4}{3x-1}$  

 $\frac{\text{d}}{\text{d}x}\left(\frac{e^{3x}}{\sin\left(2x\right)}\right)$  

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

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

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

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

 $\frac{\text{d}}{\text{d}x}\left(4e^{\left(3x-1\right)}\cos x\right)$  

•  $4e^{\left(3x-1\right)}\left(3\cos x-\sin x\right)$  

•  $4e^{\left(3x-1\right)}\left(3\cos x+\sin x\right)$  

•  $4e^{\left(3x-1\right)}\left(\cos x-\sin x\right)$  

•  $4e^{\left(3x-1\right)}\left(\cos x+\sin x\right)$