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Popular >

derivative of (x^2-7)sqrt(x)

Solution

derivative of

(x^{2} - 7) x

Solution

\frac{5 x ^{2} - 7}{2 x}

Solution steps

\frac{d}{d x} ((x^{2} - 7) x)

Apply the Product Rule:

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

f = x^{2} - 7, g = x

= \frac{d}{d x} (x^{2} - 7) x + \frac{d}{d x} (x) (x^{2} - 7)

\frac{d}{d x} (x^{2} - 7) = 2 x

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

= 2 x x + \frac{1}{2 x} (x^{2} - 7)

Simplify

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

= \frac{5 x ^{2} - 7}{2 x}

Popular Examples

limit as x approaches 0 of x/1

x \to 0 lim (\frac{x}{1})

tangent of f(x)=4x^3-4x,(1,0)tangent of

f (x) = 4 x^{3} - 4 x, (1, 0)

derivative of \sqrt[5]{8x^3+9x}

integral of (2x)/(\sqrt[3]{3x^2+6)}

normal of y=4x^3-9x^2-12x+12,(1,-5)normal of

y = 4 x^{3} - 9 x^{2} - 12 x + 12, (1, - 5)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-7)sqrt(x) ?
The derivative of (x^2-7)sqrt(x) is (5x^2-7)/(2sqrt(x))
What is the first derivative of (x^2-7)sqrt(x) ?
The first derivative of (x^2-7)sqrt(x) is (5x^2-7)/(2sqrt(x))