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

The derivative of f(x)=x^2sqrt(3x+5) is (15x^2+20x)/(2sqrt(3x+5))

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

The first derivative of f(x)=x^2sqrt(3x+5) is (15x^2+20x)/(2sqrt(3x+5))

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derivative of

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

\frac{15 x ^{2} + 20 x}{2 3 x + 5}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x 3 x + 5 + \frac{3}{2 3 x + 5} x^{2} : \frac{15 x ^{2} + 20 x}{2 3 x + 5}

= \frac{15 x ^{2} + 20 x}{2 3 x + 5}

What is the derivative of f(x)=x^2sqrt(3x+5) ?
The derivative of f(x)=x^2sqrt(3x+5) is (15x^2+20x)/(2sqrt(3x+5))
What is the first derivative of f(x)=x^2sqrt(3x+5) ?
The first derivative of f(x)=x^2sqrt(3x+5) is (15x^2+20x)/(2sqrt(3x+5))