What is the derivative of y=(3sqrt(x)+5)x^2 ?

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

What is the first derivative of y=(3sqrt(x)+5)x^2 ?

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

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derivative of

y = (3 x + 5) x^{2}

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

Solution steps

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

Apply the Product Rule:

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

f = 3 x + 5, g = x^{2}

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

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

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

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

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

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

\int \frac{x ^{2} + 5 x + 6}{x + 3} d x

y = 9 - x^{2}, y = x + 3

\int sin (6 x) d x

(- 72 sin (t))^{^{'}}

y = 2 x^{3}

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