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Popular >

derivative of (3x^2-6x+6e^x)

Solution

\frac{d}{d x} ((3 x^{2} - 6 x + 6) e^{x})

Solution

3 e^{x} x^{2}

Solution steps

\frac{d}{d x} ((3 x^{2} - 6 x + 6) e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x^{2} - 6 x + 6, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 6 x + 6) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 6 x + 6)

\frac{d}{d x} (3 x^{2} - 6 x + 6) = 6 x - 6

\frac{d}{d x} (e^{x}) = e^{x}

= (6 x - 6) e^{x} + e^{x} (3 x^{2} - 6 x + 6)

Simplify

(6 x - 6) e^{x} + e^{x} (3 x^{2} - 6 x + 6) : 3 e^{x} x^{2}

= 3 e^{x} x^{2}

Popular Examples

tangent of y=2x^3+x^2+23 tangent of

y = 2 x^{3} + x^{2} + 23

taylor cos^2(2θ)taylor

cos^{2} (2 θ)

y^'=-10y,y(0)=5

y^{^{'}} = - 10 y, y (0) = 5

2y^{''}+y^'-y=x+7

2 y^{^{''}} + y^{^{'}} - y = x + 7

limit as x approaches-infinity of x*0

x \to - \infty lim (x \cdot 0)

Frequently Asked Questions (FAQ)

What is the derivative of (3x^2-6x+6e^x) ?
The derivative of (3x^2-6x+6e^x) is 3e^xx^2
What is the first derivative of (3x^2-6x+6e^x) ?
The first derivative of (3x^2-6x+6e^x) is 3e^xx^2