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Derivatives Worksheets - Download free PDFs

Derivatives

Basic

Constant Rule

1.\:\:\frac{d}{dx}(1)

2.\:\:\frac{d}{dx}(\frac{2}{3})

3.\:\:\frac{d}{dx}(\sin(\frac{\pi}{2}))

4.\:\:\frac{d}{dx}(3a)

5.\:\:\frac{d}{dx}(n^2)^{\frac{1}{3}}

6.\:\:\frac{d}{dx}(-4)

7.\:\:\frac{d}{dx}(\sqrt{3})

8.\:\:\frac{d}{dx}(\frac{1}{2})

9.\:\:\frac{d}{dx}(6)

10.\:\:\frac{d}{dx}(a)

Derivatives

Basic

Multiplication by Constant

1.\:\:\frac{d}{dx}(3x)

2.\:\:\frac{d}{dv}(2v)

3.\:\:\frac{d}{dx}(\frac{x}{2})

4.\:\:\frac{d}{dx}(\frac{2}{3}x)

5.\:\:\frac{d}{dx}(-5x)

6.\:\:\frac{d}{dx}(-2x)

7.\:\:\frac{d}{dx}(\sqrt{5}x)

8.\:\:\frac{d}{dy}(\frac{1}{2}y)

9.\:\:\frac{d}{dy}(3\sqrt{2}y)

10.\:\:\frac{d}{dx}(ax)

Derivatives

Basic

Power Rule

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

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

3.\:\:\frac{d}{dx}(x^{-1})

4.\:\:\frac{d}{dx}(\sqrt{x})

5.\:\:\frac{d}{dx}(x^{\frac{1}{4}})

6.\:\:\frac{d}{dx}(x^5)

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

8.\:\:\frac{d}{dx}(x^{\frac{2}{3}})

9.\:\:\frac{d}{dv}(v^5)

10.\:\:\frac{d}{dv}(v^{-\frac{1}{3}})

Derivatives

Moderate

Trig Functions

1.\:\:\frac{d}{dx}(x\sin(x)+\cos(x))

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

3.\:\:\frac{d}{dx}(\frac{\sin(x)+1}{\cos(x)-1})

4.\:\:\frac{d}{dx}(\pi\cot(x))

5.\:\:\frac{d}{dx}(\tan(x)\sin(x))

6.\:\:\frac{d}{dx}(4\sin(x))

7.\:\:\frac{d}{dx}(\tan(x)-x)

8.\:\:\frac{d}{dx}(\pi\csc(x))

9.\:\:\frac{d}{dx}(\frac{\sin(x)}{2x})

10.\:\:\frac{d}{dx}(\cos(x)\sin(x))

Derivatives

Moderate

Logarithms & Exponents

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

2.\:\:\frac{d}{dx}(2\log_3(x))

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

4.\:\:\frac{d}{dx}(e^{x}+x^{e})

5.\:\:\frac{d}{dx}(\ln(x)\ln(5))

6.\:\:\frac{d}{dx}(\frac{1}{2}e^{x})

7.\:\:\frac{d}{dx}(\frac{e^{x}}{x})

8.\:\:\frac{d}{dx}(x\ln(x))

9.\:\:\frac{d}{dx}(\log_4(x))

10.\:\:\frac{d}{dx}(\ln(x)e^{x})

Derivatives

Moderate

Chain Rule

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

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

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

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

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

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

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

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

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

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

Derivatives

Advanced

Second Order

1.\:\:\frac{d^2}{dx^2}(3+x^3-5x^2-8x)

2.\:\:\frac{d^{2}}{dx^{2}}\sqrt{10-x^{2}}x

3.\:\:\frac{d^{2}}{dx^{2}}e^{x}x

4.\:\:(\sqrt{4+x})^{\prime \prime }

5.\:\:\frac{d^{2}}{dx^{2}}\frac{x^{2}}{-2+x}

6.\:\:\frac{d^2}{dx^2}\frac{\ln (x)}{10x}

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

8.\:\:\frac{d^2}{dx^2}\cos (\frac{ax}{\pi })

9.\:\:\frac{d^2}{dx^2}(\frac{9+3x}{2-x})

10.\:\:(\sin^2(θ))^{''}

Derivatives

Advanced

Higher Order

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

2.\:\:\frac{d^{3}}{dx^{3}}(6x^{3}-4x^{4})

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

4.\:\:\frac{d^{3}}{dx^{3}}e^{x^2}

5.\:\:\frac{d^4}{dy^4}(a^y)

6.\:\:\frac{d^{4}}{dx^{4}}(\frac{x-2}{x-3})

7.\:\:\frac{d^{4}}{dx^{4}}\ln(x^{2}+1)

8.\:\:\frac{d^{4}}{dx^{4}}(e^{-x^2})

9.\:\:\frac{d^{5}}{dx^{5}}(\frac{1}{e^{2x}-1})

10.\:\:\frac{d^{5}}{dx^{5}}(\sin^{-1}x)

Derivatives

Partial Derivatives

Partial Derivatives

1.\:\:\frac{\partial}{\partial x}(xy)

2.\:\:\frac{\partial}{\partial y}(\frac{x}{y})

3.\:\:\frac{\partial}{\partial x}(\ln(x^{2}+y^{2}))

4.\:\:\frac{\partial}{\partial x}(\sqrt{x^{2}+y^{2}})

5.\:\:\frac{\partial}{\partial x}(xe^{xy})

6.\:\:\frac{\partial}{\partial y}(xe^{y})

7.\:\:\frac{\partial}{\partial x}(\ln(xy))

8.\:\:\frac{\partial}{\partial x}(e^{xy})

9.\:\:\frac{\partial}{\partial x}(xe^{y})

10.\:\:\frac{\partial}{\partial x}(13x^{5}-7x^{2}+8y^{3}+2x^{2}y^{2})