What is the derivative of x^{2-3x}x^2 ?

The derivative of x^{2-3x}x^2 is -3x^{-3x+4}ln(x)+4x^{-3x+3}-3x^{-3x+4}

What is the first derivative of x^{2-3x}x^2 ?

The first derivative of x^{2-3x}x^2 is -3x^{-3x+4}ln(x)+4x^{-3x+3}-3x^{-3x+4}

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

- 3 x^{- 3 x + 4} ln (x) + 4 x^{- 3 x + 3} - 3 x^{- 3 x + 4}

Solution steps

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

Apply the Product Rule:

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

f = x^{2 - 3 x}, g = x^{2}

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

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

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

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

Simplify

x^{2 - 3 x} (- 3 ln (x) + \frac{2 - 3 x}{x}) x^{2} + 2 x x^{2 - 3 x} : - 3 x^{- 3 x + 4} ln (x) + 4 x^{- 3 x + 3} - 3 x^{- 3 x + 4}

= - 3 x^{- 3 x + 4} ln (x) + 4 x^{- 3 x + 3} - 3 x^{- 3 x + 4}

i = 1 \sum \infty i

x \to - 7 lim (\frac{- x ^{2}}{x + 7})

\int \frac{1}{( x + 7 ) ^{2}} d x

\int - 8 sin (8 x) d x

y = 6 x + \frac{4}{3}

What is the derivative of x^{2-3x}x^2 ?
The derivative of x^{2-3x}x^2 is -3x^{-3x+4}ln(x)+4x^{-3x+3}-3x^{-3x+4}
What is the first derivative of x^{2-3x}x^2 ?
The first derivative of x^{2-3x}x^2 is -3x^{-3x+4}ln(x)+4x^{-3x+3}-3x^{-3x+4}