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Popular >

derivative of f(x)=4x^{5/4}+8x^{3/2}+2x

Solution

derivative of

f (x) = 4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 2 x

Solution

5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 2

Solution steps

\frac{d}{d x} (4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 2 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x^{\frac{5}{4}}) + \frac{d}{d x} (8 x^{\frac{3}{2}}) + \frac{d}{d x} (2 x)

\frac{d}{d x} (4 x^{\frac{5}{4}}) = 5 x^{\frac{1}{4}}

\frac{d}{d x} (8 x^{\frac{3}{2}}) = 12 x^{\frac{1}{2}}

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

= 5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 2

Popular Examples

tangent of f(x)= 2/(sqrt(x)),\at 1/16 tangent of

f (x) = \frac{2}{x}, at \frac{1}{16}

derivative of ((x^2+x)/(x^2))

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

integral of (x^5-10x^4+x^3-15x^2)

\int (x^{5} - 10 x^{4} + x^{3} - 15 x^{2}) d x

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

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

integral of e^{x^4}x^3

\int e^{x^{4}} x^{3} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=4x^{5/4}+8x^{3/2}+2x ?
The derivative of f(x)=4x^{5/4}+8x^{3/2}+2x is 5x^{1/4}+12x^{1/2}+2
What is the first derivative of f(x)=4x^{5/4}+8x^{3/2}+2x ?
The first derivative of f(x)=4x^{5/4}+8x^{3/2}+2x is 5x^{1/4}+12x^{1/2}+2