What is the derivative of ax^2(x-4+bx^4ln(x/4)) ?

The derivative of ax^2(x-4+bx^4ln(x/4)) is a(3x^2-8x)+b(4x^3ln(x/4)+x^3)

What is the first derivative of ax^2(x-4+bx^4ln(x/4)) ?

The first derivative of ax^2(x-4+bx^4ln(x/4)) is a(3x^2-8x)+b(4x^3ln(x/4)+x^3)

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\frac{d}{d x} (a x^{2} (x - 4) + b x^{4} ln (\frac{x}{4}))

a (3 x^{2} - 8 x) + b (4 x^{3} ln (\frac{x}{4}) + x^{3})

Solution steps

\frac{d}{d x} (a x^{2} (x - 4) + b x^{4} ln (\frac{x}{4}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a x^{2} (x - 4)) + \frac{d}{d x} (b x^{4} ln (\frac{x}{4}))

\frac{d}{d x} (a x^{2} (x - 4)) = a (3 x^{2} - 8 x)

\frac{d}{d x} (b x^{4} ln (\frac{x}{4})) = b (4 x^{3} ln (\frac{x}{4}) + x^{3})

= a (3 x^{2} - 8 x) + b (4 x^{3} ln (\frac{x}{4}) + x^{3})

\int x^{4} ln (x^{5}) d x

\frac{d y}{d x} = 2 y - x y^{2}

\frac{d}{d x} ((2 x - 1) sin (x - 2))

y = \frac{5}{ln ( x )}

f^{^{''}} (x) = e^{x}

What is the derivative of ax^2(x-4+bx^4ln(x/4)) ?
The derivative of ax^2(x-4+bx^4ln(x/4)) is a(3x^2-8x)+b(4x^3ln(x/4)+x^3)
What is the first derivative of ax^2(x-4+bx^4ln(x/4)) ?
The first derivative of ax^2(x-4+bx^4ln(x/4)) is a(3x^2-8x)+b(4x^3ln(x/4)+x^3)