Quiz about Differentiation of Composite Functions

Question 1

$$find\ the\ derivative\ of\ \sin\left(x^2\ +5\right)$$

Accepted Answer

$$2x\cos\left(x^2\ +5\right)$$

Answer

cos(2x)

Answer

$$\cos\left(x^2+\ 5\right)$$

Answer

$$-2x\cos\left(x^2+5\right)$$

Question 2

derivative of cos(sinx)

Accepted Answer

-cosx.sin(sinx)

Answer

-sin(sinx)

Answer

-sin(cosx)

Answer

cosx. sin(sinx)

Question 3

$$derivative\ of\ \operatorname{cosec}\left(x^3\right)$$ =

Accepted Answer

$$-3x^2\operatorname{cosec}(x^3)\cot(x^3)$$

Answer

$$3x^2\operatorname{cosec}(x^3)\cot(x^3)$$

Answer

$$-3x^2\operatorname{cosec}(3x^2)\cot(3x^2)$$

Answer

None of these

Question 4

$$derivative\ of\ \left(x\ +4\right)^{\frac{3}{4}}$$

Accepted Answer

$$\frac{3}{4\left(x+4\right)^{\frac{1}{4}}}$$

Answer

$$\frac{6x}{4\left(x^2+4\right)^{\frac{1}{4}}}$$

Answer

$$\frac{3}{4\left(x+4\right)^{\frac{7}{4}}}$$

Answer

none of these

Question 5

The derivative of sin(2x)

Accepted Answer

2cos(2x)

Answer

2cos(x)

Answer

2sin(2x)

Answer

2xcos(2x)

Question 6

The derivative of xcos(2x²)

Accepted Answer

cos(2x²) - 4x²sin(2x²)

Answer

sin(2x²) - 4x²cos(2x²)

Answer

cos(2x²) + 4x²sin(2x²)

Answer

cos(2x²) - 2x²cos(2x²)

Question 7

$$If\ y\ =\sec\sqrt{x\ }\ then\ \frac{dy}{dx}=?$$

Accepted Answer

$$\frac{\sec\sqrt{x}. an\sqrt{x}}{2\sqrt{x}}$$

Answer

$$\frac{ an^2\sqrt{x}}{\sqrt{x}}$$

Answer

$$\frac{ an\sqrt{x}}{2\sqrt{x}}$$

Answer

$$\sec\sqrt{x}. an\sqrt{x}.2\sqrt{x}$$

Question 8

$$If\ y=\cos\left(x^2e^x\right)\ then\ \frac{dy}{dx}=?$$

Accepted Answer

$$-\sin\left(x^2e^x\right).\left(x^2e^x+2xe^x\ \right)$$

Answer

$$-\sin\left(x^2e^x\right).\left(2x+e^x\right)$$

Answer

$$\sin\left(x^2e^x\right)\left(x^2e^{x\ }+2xe^x\right)$$

Answer

$$NONE$$

Question 9

$$differentiate\ \cos\left(\log x\ +\ e^x\right)$$

Accepted Answer

$$-\frac{1}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$$

Answer

$$\frac{1}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$$

Answer

$$-\frac{e^x}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$$

Answer

$$-\frac{1}{x}\cos\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$$

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