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Popular >

derivative of f(x)=4x^{5/4}+6x^{3/2}+3x

Solution

derivative of

f (x) = 4 x^{\frac{5}{4}} + 6 x^{\frac{3}{2}} + 3 x

Solution

5 x^{\frac{1}{4}} + 9 x^{\frac{1}{2}} + 3

Solution steps

\frac{d}{d x} (4 x^{\frac{5}{4}} + 6 x^{\frac{3}{2}} + 3 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} (6 x^{\frac{3}{2}}) + \frac{d}{d x} (3 x)

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

\frac{d}{d x} (6 x^{\frac{3}{2}}) = 9 x^{\frac{1}{2}}

\frac{d}{d x} (3 x) = 3

= 5 x^{\frac{1}{4}} + 9 x^{\frac{1}{2}} + 3

Popular Examples

y^{''}+12y^'+36y=0,y(1)=0,y^'(1)=1

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (1) = 0, y^{^{'}} (1) = 1

derivative of 2^{60}derivative of

2^{60}

y^'=(2xy-y^4)/(3x^2)

y^{^{'}} = \frac{2 x y - y ^{4}}{3 x ^{2}}

derivative of f(x)=sqrt(x)(x-10)derivative of

f (x) = x (x - 10)

5y^{''}+32y=0,y(0)=8,y^'(0)=5

5 y^{^{''}} + 32 y = 0, y (0) = 8, y^{^{'}} (0) = 5

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=4x^{5/4}+6x^{3/2}+3x ?
The derivative of f(x)=4x^{5/4}+6x^{3/2}+3x is 5x^{1/4}+9x^{1/2}+3
What is the first derivative of f(x)=4x^{5/4}+6x^{3/2}+3x ?
The first derivative of f(x)=4x^{5/4}+6x^{3/2}+3x is 5x^{1/4}+9x^{1/2}+3