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Moderate Chain Rule Worksheets

Derivatives

Moderate

Chain Rule

1. \frac{d}{dx}(\cos(2x))

1. \frac{d}{dx}(\cos(2x))

2. \frac{d}{dx}(\sqrt{2x^2+5})

2. \frac{d}{dx}(\sqrt{2x^2+5})

3. \frac{d}{dx}(3^{x})

3. \frac{d}{dx}(3^{x})

4. \frac{d}{dx}(\sin^2(x))

4. \frac{d}{dx}(\sin^2(x))

5. \frac{d}{dx}(e^{x^2})

5. \frac{d}{dx}(e^{x^2})

6. \frac{d}{dx}(\ln(x^2-5x))

6. \frac{d}{dx}(\ln(x^2-5x))

7. \frac{d}{dx}(\sqrt{2x^2-1})

7. \frac{d}{dx}(\sqrt{2x^2-1})

8. \frac{d}{dx}((4x-3)^3)

8. \frac{d}{dx}((4x-3)^3)

9. \frac{d}{dx}((2x+6)^2)

9. \frac{d}{dx}((2x+6)^2)

10. \frac{d}{dx}(\tan(2x))

10. \frac{d}{dx}(\tan(2x))

Answers

Derivatives

Moderate

Chain Rule

1. -\sin(2x)\cdot 2

2. \frac{2x}{\sqrt{2x^{2}+5}}

3. 3^{x}\ln(3)

4. \sin(2x)

5. e^{x^{2}}\cdot 2x

6. \frac{2x-5}{x^{2}-5x}

7. \frac{2x}{\sqrt{2x^{2}-1}}

8. 12(4x-3)^{2}

9. 4(2x+6)

10. \sec^{2}(2x)\cdot 2