What is the derivative of f(x)=x^2sqrt(4x-1) ?

The derivative of f(x)=x^2sqrt(4x-1) is (10x^2-2x)/(sqrt(4x-1))

What is the first derivative of f(x)=x^2sqrt(4x-1) ?

The first derivative of f(x)=x^2sqrt(4x-1) is (10x^2-2x)/(sqrt(4x-1))

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derivative of

f (x) = x^{2} 4 x - 1

\frac{10 x ^{2} - 2 x}{4 x - 1}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = 4 x - 1

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

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

\frac{d}{d x} (4 x - 1) = \frac{2}{4 x - 1}

= 2 x 4 x - 1 + \frac{2}{4 x - 1} x^{2}

Simplify

2 x 4 x - 1 + \frac{2}{4 x - 1} x^{2} : \frac{10 x ^{2} - 2 x}{4 x - 1}

= \frac{10 x ^{2} - 2 x}{4 x - 1}

g (x) = \frac{1}{4 x ^{2} + 5 x}

sin (5 t - \frac{π}{3}) \cdot 1 (5 t - \frac{π}{3})

\frac{3 z - 5}{z ^{2} - 4 z + 3}

\int_{1}^{3} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x

(3 x + 2 y) d x + (2 x + y) d y = 0

What is the derivative of f(x)=x^2sqrt(4x-1) ?
The derivative of f(x)=x^2sqrt(4x-1) is (10x^2-2x)/(sqrt(4x-1))
What is the first derivative of f(x)=x^2sqrt(4x-1) ?
The first derivative of f(x)=x^2sqrt(4x-1) is (10x^2-2x)/(sqrt(4x-1))