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Derivative of $$$e^{x} + \sin{\left(y z \right)}$$$ with respect to $$$x$$$

The calculator will find the derivative of $$$e^{x} + \sin{\left(y z \right)}$$$ with respect to $$$x$$$, with steps shown.

Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps

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Your Input

Find $$$\frac{d}{dx} \left(e^{x} + \sin{\left(y z \right)}\right)$$$.

Solution

The derivative of a sum/difference is the sum/difference of derivatives:

$${\color{red}\left(\frac{d}{dx} \left(e^{x} + \sin{\left(y z \right)}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(e^{x}\right) + \frac{d}{dx} \left(\sin{\left(y z \right)}\right)\right)}$$

The derivative of the exponential is $$$\frac{d}{dx} \left(e^{x}\right) = e^{x}$$$:

$${\color{red}\left(\frac{d}{dx} \left(e^{x}\right)\right)} + \frac{d}{dx} \left(\sin{\left(y z \right)}\right) = {\color{red}\left(e^{x}\right)} + \frac{d}{dx} \left(\sin{\left(y z \right)}\right)$$

The derivative of a constant is $$$0$$$:

$$e^{x} + {\color{red}\left(\frac{d}{dx} \left(\sin{\left(y z \right)}\right)\right)} = e^{x} + {\color{red}\left(0\right)}$$

Thus, $$$\frac{d}{dx} \left(e^{x} + \sin{\left(y z \right)}\right) = e^{x}$$$.

Answer

$$$\frac{d}{dx} \left(e^{x} + \sin{\left(y z \right)}\right) = e^{x}$$$A

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function