What is the derivative of y=(x+9)(3sqrt(x)+4) ?

The derivative of y=(x+9)(3sqrt(x)+4) is (9x+27)/(2sqrt(x))+4

What is the first derivative of y=(x+9)(3sqrt(x)+4) ?

The first derivative of y=(x+9)(3sqrt(x)+4) is (9x+27)/(2sqrt(x))+4

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derivative of

y = (x + 9) (3 x + 4)

\frac{9 x + 27}{2 x} + 4

Solution steps

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

Apply the Product Rule:

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

f = x + 9, g = 3 x + 4

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

\frac{d}{d x} (x + 9) = 1

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

= 1 \cdot (3 x + 4) + \frac{3}{2 x} (x + 9)

Simplify

1 \cdot (3 x + 4) + \frac{3}{2 x} (x + 9) : \frac{9 x + 27}{2 x} + 4

= \frac{9 x + 27}{2 x} + 4

\int (3 x - 2 3 x) d x

5

\int (x - 3 y^{2}) d y

\frac{d}{d x} (\frac{tan ( x )}{6 x sec ( x )})

\frac{\partial}{\partial x} (se x)

What is the derivative of y=(x+9)(3sqrt(x)+4) ?
The derivative of y=(x+9)(3sqrt(x)+4) is (9x+27)/(2sqrt(x))+4
What is the first derivative of y=(x+9)(3sqrt(x)+4) ?
The first derivative of y=(x+9)(3sqrt(x)+4) is (9x+27)/(2sqrt(x))+4