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Popular >

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

Solution

derivative of

y = 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}

Graph

Popular Examples

integral of (5x)/(sqrt(3x^2+4))

\int \frac{5 x}{3 x ^{2} + 4} d x

sum from n=0 to infinity of 5(3/2)^n

n = 0 \sum \infty 5 (\frac{3}{2})^{n}

integral of x^2sqrt(8x+9)

\int x^{2} 8 x + 9 d x

(\partial)/(\partial y)((y^3)/(x^2+y^2))

\frac{\partial}{\partial y} (\frac{y ^{3}}{x ^{2} + y ^{2}})

sum from n=0 to infinity of (3n^9)/(n!)

n = 0 \sum \infty \frac{3 n ^{9}}{n !}

Frequently Asked Questions (FAQ)

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