What is the derivative of sqrt(x)(3x^2+4x-9) ?

The derivative of sqrt(x)(3x^2+4x-9) is (15x^2+12x-9)/(2sqrt(x))

What is the first derivative of sqrt(x)(3x^2+4x-9) ?

The first derivative of sqrt(x)(3x^2+4x-9) is (15x^2+12x-9)/(2sqrt(x))

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\frac{d}{d x} (x (3 x^{2} + 4 x - 9))

\frac{15 x ^{2} + 12 x - 9}{2 x}

Solution steps

\frac{d}{d x} (x (3 x^{2} + 4 x - 9))

Apply the Product Rule:

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

f = x, g = 3 x^{2} + 4 x - 9

= \frac{d}{d x} (x) (3 x^{2} + 4 x - 9) + \frac{d}{d x} (3 x^{2} + 4 x - 9) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (3 x^{2} + 4 x - 9) = 6 x + 4

= \frac{1}{2 x} (3 x^{2} + 4 x - 9) + (6 x + 4) x

Simplify

\frac{1}{2 x} (3 x^{2} + 4 x - 9) + (6 x + 4) x : \frac{15 x ^{2} + 12 x - 9}{2 x}

= \frac{15 x ^{2} + 12 x - 9}{2 x}

y^{^{''}} + 9 y = 5 t^{4}, y (0) = 0, y^{^{'}} (0) = 0

\frac{d}{d x} (arcsech (x))

\frac{\partial}{\partial x} (6 x^{\frac{1}{2}} + 2 y)

x \to 0 lim (sin (x) ln (4 x))

What is the derivative of sqrt(x)(3x^2+4x-9) ?
The derivative of sqrt(x)(3x^2+4x-9) is (15x^2+12x-9)/(2sqrt(x))
What is the first derivative of sqrt(x)(3x^2+4x-9) ?
The first derivative of sqrt(x)(3x^2+4x-9) is (15x^2+12x-9)/(2sqrt(x))