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Popular >

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

Solution

derivative of

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

Solution

\frac{3 x ^{\frac{1}{2}}}{2} + \frac{1}{2 ( x + 4 ) ^{\frac{1}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (x + 4) = \frac{1}{2 ( x + 4 ) ^{\frac{1}{2}}}

= \frac{3 x ^{\frac{1}{2}}}{2} + \frac{1}{2 ( x + 4 ) ^{\frac{1}{2}}}

Graph

Popular Examples

tangent of xe^x tangent of

x e^{x}

limit as x approaches 0 of tan(4x)

x \to 0 lim (tan (4 x))

y^{''}-4y^'-5y=0,y(-1)=3,y^'(-1)=9

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3, y^{^{'}} (- 1) = 9

derivative of 4e^{4e^x+x}

\frac{d}{d x} (4 e^{4 e^{x} + x})

derivative of f(x)=(-x^2-4)/((x^2-4)^2)derivative of

f (x) = \frac{- x ^{2} - 4}{( x ^{2} - 4 ) ^{2}}

Frequently Asked Questions (FAQ)

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