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

The derivative of 3x^2sqrt(5x+3) is (3(25x^2+12x))/(2sqrt(5x+3))

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

The first derivative of 3x^2sqrt(5x+3) is (3(25x^2+12x))/(2sqrt(5x+3))

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

\frac{3 ( 25 x ^{2} + 12 x )}{2 5 x + 3}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 (2 x 5 x + 3 + \frac{5}{2 5 x + 3} x^{2}) : \frac{3 ( 25 x ^{2} + 12 x )}{2 5 x + 3}

= \frac{3 ( 25 x ^{2} + 12 x )}{2 5 x + 3}

f (x) = 2 - 10 x, at x = - 1

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\int \frac{x ^{3}}{( 1 + x ^{4} )} d x

What is the derivative of 3x^2sqrt(5x+3) ?
The derivative of 3x^2sqrt(5x+3) is (3(25x^2+12x))/(2sqrt(5x+3))
What is the first derivative of 3x^2sqrt(5x+3) ?
The first derivative of 3x^2sqrt(5x+3) is (3(25x^2+12x))/(2sqrt(5x+3))