What is the derivative of ax^5ln(x/2+bx^3(x-2)) ?

The derivative of ax^5ln(x/2+bx^3(x-2)) is a(5x^4ln(x/2)+x^4)+b(4x^3-6x^2)

What is the first derivative of ax^5ln(x/2+bx^3(x-2)) ?

The first derivative of ax^5ln(x/2+bx^3(x-2)) is a(5x^4ln(x/2)+x^4)+b(4x^3-6x^2)

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\frac{d}{d x} (a x^{5} ln (\frac{x}{2}) + b x^{3} (x - 2))

a (5 x^{4} ln (\frac{x}{2}) + x^{4}) + b (4 x^{3} - 6 x^{2})

Solution steps

\frac{d}{d x} (a x^{5} ln (\frac{x}{2}) + b x^{3} (x - 2))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a x^{5} ln (\frac{x}{2})) + \frac{d}{d x} (b x^{3} (x - 2))

\frac{d}{d x} (a x^{5} ln (\frac{x}{2})) = a (5 x^{4} ln (\frac{x}{2}) + x^{4})

\frac{d}{d x} (b x^{3} (x - 2)) = b (4 x^{3} - 6 x^{2})

= a (5 x^{4} ln (\frac{x}{2}) + x^{4}) + b (4 x^{3} - 6 x^{2})

\int \frac{1 + 2 x + x ^{2}}{3 x + 3 x ^{2} + x ^{3}} d x

f (x) = x^{6} ln (x)

f (x) = - 4 sin (2 x)

t^{2} y^{^{''}} - 3 t y^{^{'}} - 21 y = 0

\frac{\partial}{\partial y} (x^{2} y e^{\frac{y}{z}})

What is the derivative of ax^5ln(x/2+bx^3(x-2)) ?
The derivative of ax^5ln(x/2+bx^3(x-2)) is a(5x^4ln(x/2)+x^4)+b(4x^3-6x^2)
What is the first derivative of ax^5ln(x/2+bx^3(x-2)) ?
The first derivative of ax^5ln(x/2+bx^3(x-2)) is a(5x^4ln(x/2)+x^4)+b(4x^3-6x^2)