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Derivative of 2y2 y

The calculator will find the derivative of 2y2 y, with steps shown.

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

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Your Input

Find ddy(2y)\frac{d}{dy} \left(2 y\right).

Solution

Apply the constant multiple rule ddy(cf(y))=cddy(f(y))\frac{d}{dy} \left(c f{\left(y \right)}\right) = c \frac{d}{dy} \left(f{\left(y \right)}\right) with c=2c = 2 and f(y)=yf{\left(y \right)} = y:

(ddy(2y))=(2ddy(y)){\color{red}\left(\frac{d}{dy} \left(2 y\right)\right)} = {\color{red}\left(2 \frac{d}{dy} \left(y\right)\right)}

Apply the power rule ddy(yn)=nyn−1\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1} with n=1n = 1, in other words, ddy(y)=1\frac{d}{dy} \left(y\right) = 1:

2(ddy(y))=2(1)2 {\color{red}\left(\frac{d}{dy} \left(y\right)\right)} = 2 {\color{red}\left(1\right)}

Thus, ddy(2y)=2\frac{d}{dy} \left(2 y\right) = 2.

Answer

ddy(2y)=2\frac{d}{dy} \left(2 y\right) = 2A

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