What is the derivative of f(x)=7x^3sqrt(x) ?

The derivative of f(x)=7x^3sqrt(x) is (49x^{5/2})/2

What is the first derivative of f(x)=7x^3sqrt(x) ?

The first derivative of f(x)=7x^3sqrt(x) is (49x^{5/2})/2

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derivative of

f (x) = 7 x^{3} x

\frac{49 x ^{\frac{5}{2}}}{2}

Solution steps

\frac{d}{d x} (7 x^{3} x)

Simplify

7 x^{3} x : 7 x^{\frac{7}{2}}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 7 \cdot \frac{7}{2} x^{\frac{7}{2} - 1}

Simplify

7 \cdot \frac{7}{2} x^{\frac{7}{2} - 1} : \frac{49 x ^{\frac{5}{2}}}{2}

= \frac{49 x ^{\frac{5}{2}}}{2}

f (x) = \frac{x - 1}{x - 2}, at x = 3

\int \frac{( sin ( 2 x ) )}{cos ( x )} d x

y^{^{'}} + 2 y = 18

\int \frac{6 e ^{2 x}}{e ^{2 x} + 10 e ^{x} + 16} d x

(1 - x) e^{- x}

What is the derivative of f(x)=7x^3sqrt(x) ?
The derivative of f(x)=7x^3sqrt(x) is (49x^{5/2})/2
What is the first derivative of f(x)=7x^3sqrt(x) ?
The first derivative of f(x)=7x^3sqrt(x) is (49x^{5/2})/2