What is the derivative of f(x)=(5sqrt(x)+9)x^2 ?

The derivative of f(x)=(5sqrt(x)+9)x^2 is (5x^{3/2})/2+2x(5sqrt(x)+9)

What is the first derivative of f(x)=(5sqrt(x)+9)x^2 ?

The first derivative of f(x)=(5sqrt(x)+9)x^2 is (5x^{3/2})/2+2x(5sqrt(x)+9)

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derivative of

f (x) = (5 x + 9) x^{2}

\frac{5 x ^{\frac{3}{2}}}{2} + 2 x (5 x + 9)

Solution steps

\frac{d}{d x} ((5 x + 9) x^{2})

Apply the Product Rule:

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

f = 5 x + 9, g = x^{2}

= \frac{d}{d x} (5 x + 9) x^{2} + \frac{d}{d x} (x^{2}) (5 x + 9)

\frac{d}{d x} (5 x + 9) = \frac{5}{2 x}

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

= \frac{5}{2 x} x^{2} + 2 x (5 x + 9)

\frac{5}{2 x} x^{2} = \frac{5 x ^{\frac{3}{2}}}{2}

= \frac{5 x ^{\frac{3}{2}}}{2} + 2 x (5 x + 9)

\frac{3}{x}, at x = \frac{1}{16}

\frac{d y}{d t} = y cos (3 t + 2)

x, 0, 0.5

\int e^{b} sin (t - b) d b

\int_{x}^{x} 1 d t

What is the derivative of f(x)=(5sqrt(x)+9)x^2 ?
The derivative of f(x)=(5sqrt(x)+9)x^2 is (5x^{3/2})/2+2x(5sqrt(x)+9)
What is the first derivative of f(x)=(5sqrt(x)+9)x^2 ?
The first derivative of f(x)=(5sqrt(x)+9)x^2 is (5x^{3/2})/2+2x(5sqrt(x)+9)