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

The derivative of (3sqrt(x)+4x^2) is (3x^{3/2})/2+2x(3sqrt(x)+4)

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

The first derivative of (3sqrt(x)+4x^2) is (3x^{3/2})/2+2x(3sqrt(x)+4)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

\int \frac{1}{n ^{2} + 1}

\int x cos (x y) d y

\frac{d}{d x} (ln (4 x^{2} + 1))

\frac{d}{d x} (1000 (1 - e^{- 0.15 x}))

3^{x} lo g_{3} (x)

What is the derivative of (3sqrt(x)+4x^2) ?
The derivative of (3sqrt(x)+4x^2) is (3x^{3/2})/2+2x(3sqrt(x)+4)
What is the first derivative of (3sqrt(x)+4x^2) ?
The first derivative of (3sqrt(x)+4x^2) is (3x^{3/2})/2+2x(3sqrt(x)+4)