What is the derivative of 6x^{7/2}+4x^{5/2}+2x ?

The derivative of 6x^{7/2}+4x^{5/2}+2x is 21x^{5/2}+10x^{3/2}+2

What is the first derivative of 6x^{7/2}+4x^{5/2}+2x ?

The first derivative of 6x^{7/2}+4x^{5/2}+2x is 21x^{5/2}+10x^{3/2}+2

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\frac{d}{d x} (6 x^{\frac{7}{2}} + 4 x^{\frac{5}{2}} + 2 x)

21 x^{\frac{5}{2}} + 10 x^{\frac{3}{2}} + 2

Solution steps

\frac{d}{d x} (6 x^{\frac{7}{2}} + 4 x^{\frac{5}{2}} + 2 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (6 x^{\frac{7}{2}}) + \frac{d}{d x} (4 x^{\frac{5}{2}}) + \frac{d}{d x} (2 x)

\frac{d}{d x} (6 x^{\frac{7}{2}}) = 21 x^{\frac{5}{2}}

\frac{d}{d x} (4 x^{\frac{5}{2}}) = 10 x^{\frac{3}{2}}

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

= 21 x^{\frac{5}{2}} + 10 x^{\frac{3}{2}} + 2

What is the derivative of 6x^{7/2}+4x^{5/2}+2x ?
The derivative of 6x^{7/2}+4x^{5/2}+2x is 21x^{5/2}+10x^{3/2}+2
What is the first derivative of 6x^{7/2}+4x^{5/2}+2x ?
The first derivative of 6x^{7/2}+4x^{5/2}+2x is 21x^{5/2}+10x^{3/2}+2