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Popular >

derivative of sqrt(x)*5x^2

Solution

derivative of

x \cdot 5 x^{2}

Solution

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

Solution steps

\frac{d}{d x} (x \cdot 5 x^{2})

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = x^{2}

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

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

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

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

\frac{1}{2 x} x^{2} = \frac{x ^{\frac{3}{2}}}{2}

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

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\int \frac{1}{1 + cos ^{2} ( θ )} d θ

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\frac{d}{d x} (arccos (sin (x^{2} + 9 x)))

derivative of f(x)=sqrt(3x+4)derivative of

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x \to 0 lim ((1 + \frac{3}{x})^{x})

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)*5x^2 ?
The derivative of sqrt(x)*5x^2 is 5((x^{3/2})/2+2xsqrt(x))
What is the first derivative of sqrt(x)*5x^2 ?
The first derivative of sqrt(x)*5x^2 is 5((x^{3/2})/2+2xsqrt(x))