Quiz about REGLAS DE LA DERIVADA Y REGLA DE LA CADENA

Question 1

Hallar la derivada de $$f\left(x\right)=\left(3x^2-5x\right)^3$$

Accepted Answer

$$\left(18x-15\right)\left(3x^2-5x\right)^2$$

Answer

$$(18x−15)^2(3x^2−5x)^2$$

Answer

$$(18x−15)(3x^2−5x)^3$$

Answer

$$(18x−15)(3x−5)^2$$

Question 2

Hallar la derivada de $$y=\left(x+3\right)^2$$

Accepted Answer

$$2x+6$$

Answer

$$2x$$

Answer

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

Question 3

Hallar la derivada de $$f\left(x\right)=\left(2x-3\right)^5\left(x^2+4x\right)^6$$

Accepted Answer

$$\left(2x-3\right)^4\left(x^2+4x\right)^5\left(34x^2-52x-72\right)$$

Answer

$$\left(2x-3\right)^5\left(x^2+4x\right)^6\left(34x^2-52x-72\right)$$

Answer

$$\left(2x-3\right)^4\left(x^2+4x\right)^5\left(34x^2-72x-52\right)$$

Question 4

$$f\left(t\right)=\left(\frac{t^3-2t+1}{t^4+3}\right)^{13}$$ Hallar la derivada

Accepted Answer

$$13\left(\frac{t^3-2t+1}{t^4+3}\right)^{12}\left(\frac{-t^6+6t-4t^3+9t^2-6}{\left(t^4+3\right)^2}\right)$$

Answer

$$13\left(\frac{t^3-2t+1}{t^4+3}\right)^{13}\left(\frac{-t^6+6t-4t^3+9t^2-6}{\left(t^4+3\right)^3}\right)$$

Answer

$$12\left(\frac{t^3-2t+1}{t^4+3}\right)^{13}\left(\frac{-t^6+6t-4t^3+9t^2-6}{\left(t^4+3\right)^2}\right)$$

Question 5

Hallar la derivada de $$y=\left(x+3\right)^2$$

Accepted Answer

$$2x+6$$

Answer

$$2x$$

Answer

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

Question 6

Hallar la derivada $$f\left(x\right)=\frac{x^2\left(1-x\right)^3}{1+x}$$

Accepted Answer

$$\frac{\left(1+x\right)\left(1-x\right)^2x\left(2-5x\right)-x^2\left(1-x\right)^3}{\left(1+x\right)^2}$$

Answer

$$\frac{\left(1+x\right)\left(1-x\right)^{ }x\left(2-5x\right)-x^2\left(1-x\right)^2}{\left(1+x\right)^2}$$

Answer

$$\frac{\left(1+x\right)\left(1-x\right)^{ }x\left(2-5x\right)-x^{ }\left(1-x\right)^3}{\left(1+x\right)^2}$$

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