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

The derivative of f(x)=(x^3+5x^2-3)sqrt(x) is (7x^3+25x^2-3)/(2sqrt(x))

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

The first derivative of f(x)=(x^3+5x^2-3)sqrt(x) is (7x^3+25x^2-3)/(2sqrt(x))

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derivative of

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

\frac{7 x ^{3} + 25 x ^{2} - 3}{2 x}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{3} + 5 x^{2} - 3) = 3 x^{2} + 10 x

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

= (3 x^{2} + 10 x) x + \frac{1}{2 x} (x^{3} + 5 x^{2} - 3)

Simplify

(3 x^{2} + 10 x) x + \frac{1}{2 x} (x^{3} + 5 x^{2} - 3) : \frac{7 x ^{3} + 25 x ^{2} - 3}{2 x}

= \frac{7 x ^{3} + 25 x ^{2} - 3}{2 x}

(cos (3 x))^{^{'}}

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

\frac{d y}{d x} = e^{- x^{2}}

\int sech^{6} (x) tanh (x) d x

\frac{\partial}{\partial x} (\frac{x - y}{x ^{2} + y + 1})

What is the derivative of f(x)=(x^3+5x^2-3)sqrt(x) ?
The derivative of f(x)=(x^3+5x^2-3)sqrt(x) is (7x^3+25x^2-3)/(2sqrt(x))
What is the first derivative of f(x)=(x^3+5x^2-3)sqrt(x) ?
The first derivative of f(x)=(x^3+5x^2-3)sqrt(x) is (7x^3+25x^2-3)/(2sqrt(x))