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If y f u and u gx then dx du du dy dx dy.

Derivative formula 1x. You can also check your answers. 2 fracddxxn nxn 1 is called the power rule of derivatives. 1 1 csc 2 1 x x x dx d the chain rule.

Write ln x as lnx 5. The derivative calculator supports computing first second fifth derivatives as well as differentiating functions with many variables partial derivatives implicit differentiation and calculating rootszeros. Here are useful rules to help you work out the derivatives of many functions with examples below.

1 x x dx d 22. Learn all the derivative formulas here. 3 fracddxx 1 4 fracddxfxn nfxn 1.

1 1 cot 2 1 x x dx d 23. Type in any function derivative to get the solution steps and graph. Differentiate using the chain rule which states that is where and.

The slope of a line like 2x is 2 or 3x is 3 etc. Interactive graphsplots help visualize and better understand the functions. Sample inputs for practice.

If y f inside stuff then f dx dy inside stuff unchanged derivative of inside stuff. Free derivative calculator differentiate functions with all the steps. The derivative tells us the slope of a function at any point.

There are rules we can follow to find many derivatives. Replace all occurrences of with. The slope of a constant value like 3 is always 0.

Tap for more steps. Write sin 1 x as asinx 2. To apply the chain rule set as.

Are given at byjus. Derivative is the important tool in calculus to find an infinitesimal rate of change of a function with respect to its one of the independent variable. Differentiate using the power rule which states that is where.

Basic derivatives chain rule of derivatives derivative of the inverse function derivative of trigonometric functions etc.

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$1 . \dfrac{d}{dx}(c ) = o \\[3mm] 2. \dfrac{d}{dx}(x) = 1 \\[3mm] 3. \dfrac{d}{dx} (x^n) = nx^{n- 1} \\[3mm] 4. \dfrac{d}{dx}(u \pm v) = \dfrac{du}{dx} \pm \dfrac{dv}{dx} \\[3mm] 5. \dfrac{d}{dx}(cu) = c\dfrac{du}{dx} \\[3mm] 6. \dfrac{d}{dx}(uv) = u \dfrac{dv}{dx} + v \dfrac{du}{dx} \\[3mm] 7. \dfrac{d}{dx}\left(\dfrac{u}{v} \right) = \dfrac{v \dfrac{du}{dx}- u \dfrac{dv}{dx}}{v^2}(\text{quotient rule}) \\[3mm] 8. \dfrac{d}{dx}(u^n) = nu^{n- 1} \dfrac{du}{dx} \\[3mm] 9. \dfrac{d}{dx}(yu, v) = \dfrac{dv}{dx} \left(\dfrac{du}{dx}, y \right) \\ 10. \dfrac{d}{dx} (u, v) = \dfrac{dv}{dx} \left(\dfrac{du}{dx}, v \right) (\text{Chain Rule}) \dfrac{du}{dx} = \dfrac{du}{dv} \dfrac{dv}{dx} \\ \text{Another similar formula is given by} \dfrac{du}{dx} = \dfrac{\dfrac{du}{dv}}{\dfrac{dx}{dv}}$

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$8. \dfrac{d}{dx}(\cos h^{-1}(u)) = \pm \dfrac{1}{\sqrt{y^2- 1}} \dfrac{du}{dx} \\[3mm] 9. \dfrac{d}{dx}(\tan h^{-1}(u)) = \pm \dfrac{1}{\sqrt{u^2- 1}}\dfrac{du}{dx} (-1 < u <1) \\[3mm] 10. \dfrac{d}{dx}(\cot h^{-1}(u)) = \dfrac{1}{1- u^2}\dfrac{du}{dx} (u >1 \,or u< -1) \\[3mm] 11. \dfrac{d}{dx}(\sec h^{-1}(u)) = \pm \dfrac{1}{-|u| \sqrt{1- u^2}} \dfrac{dy}{dx} \\[3mm] 12. \dfrac{d}{dx}(\csc h^{-1}(u)) = \pm \dfrac{1}{-|u| \sqrt{1 + u^2}} \dfrac{du}{dx}$

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