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Popular >

derivative of 3^x-3e^pi+x^3

Solution

\frac{d}{d x} (3^{x} - 3 e^{π} + x^{3})

Solution

3 x^{2} + ln (3) \cdot 3^{x}

Solution steps

\frac{d}{d x} (3^{x} - 3 e^{π} + x^{3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3^{x}) - \frac{d}{d x} (3 e^{π}) + \frac{d}{d x} (x^{3})

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

\frac{d}{d x} (3 e^{π}) = 0

\frac{d}{d x} (x^{3}) = 3 x^{2}

= 3^{x} ln (3) - 0 + 3 x^{2}

Simplify

= 3 x^{2} + ln (3) \cdot 3^{x}

Popular Examples

(\partial)/(\partial x)(x^2(e^{-xyz}))

\frac{\partial}{\partial x} (x^{2} (e^{- x yz}))

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\frac{d}{d x} ((2 x + 1) (x - 5))

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\int \frac{21 π}{2} cos (\frac{21 π x}{2}) d x

derivative of sqrt(x+2)*sin(x)

\frac{d}{d x} (x + 2 \cdot sin (x))

limit as x approaches 0 of 8/(2+e^{1/x)}

x \to 0 lim (\frac{8}{2 + e ^{\frac{1}{x}}})

Frequently Asked Questions (FAQ)

What is the derivative of 3^x-3e^pi+x^3 ?
The derivative of 3^x-3e^pi+x^3 is 3x^2+ln(3)*3^x
What is the first derivative of 3^x-3e^pi+x^3 ?
The first derivative of 3^x-3e^pi+x^3 is 3x^2+ln(3)*3^x