What is the derivative of (5sqrt(x)+7x^2) ?

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

What is the first derivative of (5sqrt(x)+7x^2) ?

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

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

\frac{5 x ^{\frac{3}{2}}}{2} + 2 x (5 x + 7)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 5 x + 7, g = x^{2}

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

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

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

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

\frac{5}{2 x} x^{2} = \frac{5 x ^{\frac{3}{2}}}{2}

= \frac{5 x ^{\frac{3}{2}}}{2} + 2 x (5 x + 7)

\frac{d}{d x} (e^{2 x} cos (x))

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

5 e^{8 t + 9}

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

y = sin^{5} (x)

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