Find $$\frac{\text{d}y}{\text{d}x}$$ of the following function: $$y=8x^3+3x^2-11$$ .

$$\frac{\text{d}y}{\text{d}x}=24x^2+6x$$

$$\frac{\text{d}y}{\text{d}x}=2x^4+3x^3-11x$$

$$\frac{\text{d}y}{\text{d}x}=8x^2+3x\ -11$$

$$\frac{\text{d}y}{\text{d}x}=16x^3+6x^2-11$$

Solve the first derivatives for, $$y=\cos\left(-2x\right)$$ .

$$\frac{\text{d}y}{\text{d}x}=2\sin\left(-2x\right)$$

$$\frac{\text{d}y}{\text{d}x}=2\sin2x$$

$$\frac{\text{d}y}{\text{d}x}=-2\sin2x$$

$$\frac{\text{d}y}{\text{d}x}=-\sin\left(-2x\right)$$

The first derivatives for, $$y=\ln\left(2+3x\right)$$ is ________.

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

$$\frac{\text{d}y}{\text{d}x}=\frac{1}{\left(2+3x\right)}$$

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

$$\frac{\text{d}y}{\text{d}x}=\frac{1}{3\left(2+3x\right)}$$

By using PRODUCT RULE, find the derivatives for $$y=5x\left(e^{2x}\right)$$ .

$$\frac{\text{d}y}{\text{d}x}=10xe^{2x}+5e^{2x}$$

$$\frac{\text{d}y}{\text{d}x}=5xe^{2x}+5e^{2x}$$

$$\frac{\text{d}y}{\text{d}x}=5xe^{2x}+10e^{2x}$$

$$\frac{\text{d}y}{\text{d}x}=10xe^{2x}+10e^{2x}$$

Find the differentiation for the following, $$y=\frac{2x^2-1}{3x+5}$$ by using QUOTIENT RULE.

$$\frac{\text{d}y}{\text{d}x}=\frac{6x^2+20x+3}{\left(3x+5\right)^2}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{18x^2+20x+3}{\left(3x+5\right)^2}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{-18x^2+20x-3}{\left(3x+5\right)^2}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{6x^2+20x-3}{\left(3x+5\right)^2}$$

By using the derivatives concept in implicit function, differentiate the following: $$y^2=-x^2+5$$ .

$$\frac{\text{d}y}{\text{d}x}=\frac{-x}{y}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{x-5}{y}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{-x}{y^2}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{-y}{x}$$

What is the value of $$\frac{\text{d}^2y}{\text{d}x^2}$$ for, $$y=3x^4-2x^3$$ if $$x=1$$ ?

$$\frac{d^2y}{\text{d}x^2}=24$$

$$\frac{d^2y}{\text{d}x^2}=12$$

DUM20132 (QUIZ 2) - UNIT 3 DIFFERENTIATION

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