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Popular >

derivative of 7x^{1/2}+x^{3/2}

Solution

\frac{d}{d x} (7 x^{\frac{1}{2}} + x^{\frac{3}{2}})

Solution

\frac{7}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2}

Solution steps

\frac{d}{d x} (7 x^{\frac{1}{2}} + x^{\frac{3}{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x^{\frac{1}{2}}) + \frac{d}{d x} (x^{\frac{3}{2}})

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

\frac{d}{d x} (x^{\frac{3}{2}}) = \frac{3 x ^{\frac{1}{2}}}{2}

= \frac{7}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2}

Popular Examples

sum from n=1 to infinity of arctan(2n)

n = 1 \sum \infty arctan (2 n)

sum from n=1 to infinity of (2^n)/(5^n)

n = 1 \sum \infty \frac{2 ^{n}}{5 ^{n}}

integral of 5/(sqrt(x^2+16))

\int \frac{5}{x ^{2} + 16} d x

area 9/(x^4),x>= 1 area

\frac{9}{x ^{4}}, x \geq 1

integral from-4 to 6 of (x/2+6)

\int_{- 4}^{6} (\frac{x}{2} + 6) d x

Frequently Asked Questions (FAQ)

What is the derivative of 7x^{1/2}+x^{3/2} ?
The derivative of 7x^{1/2}+x^{3/2} is 7/(2x^{1/2)}+(3x^{1/2})/2
What is the first derivative of 7x^{1/2}+x^{3/2} ?
The first derivative of 7x^{1/2}+x^{3/2} is 7/(2x^{1/2)}+(3x^{1/2})/2