What is the derivative of f(x)=(sqrt(x+3))(5x^2-7x) ?

The derivative of f(x)=(sqrt(x+3))(5x^2-7x) is (25x^2+39x-42)/(2sqrt(x+3))

What is the first derivative of f(x)=(sqrt(x+3))(5x^2-7x) ?

The first derivative of f(x)=(sqrt(x+3))(5x^2-7x) is (25x^2+39x-42)/(2sqrt(x+3))

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derivative of

f (x) = (x + 3) (5 x^{2} - 7 x)

\frac{25 x ^{2} + 39 x - 42}{2 x + 3}

Solution steps

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

Apply the Product Rule:

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

f = x + 3, g = 5 x^{2} - 7 x

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

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

\frac{d}{d x} (5 x^{2} - 7 x) = 10 x - 7

= \frac{1}{2 x + 3} (5 x^{2} - 7 x) + (10 x - 7) x + 3

Simplify

\frac{1}{2 x + 3} (5 x^{2} - 7 x) + (10 x - 7) x + 3 : \frac{25 x ^{2} + 39 x - 42}{2 x + 3}

= \frac{25 x ^{2} + 39 x - 42}{2 x + 3}

\int \frac{- 8 x ^{2} + 16 x + 8}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

\int_{1}^{7} x - 1 d x

\int \frac{ln ( ln ( 3 x ) )}{3 x} d x

x \to 3 lim (5 x^{3} - 3 x + x - 6)

\frac{\partial}{\partial x} (am x^{b} m y^{1 - b})

What is the derivative of f(x)=(sqrt(x+3))(5x^2-7x) ?
The derivative of f(x)=(sqrt(x+3))(5x^2-7x) is (25x^2+39x-42)/(2sqrt(x+3))
What is the first derivative of f(x)=(sqrt(x+3))(5x^2-7x) ?
The first derivative of f(x)=(sqrt(x+3))(5x^2-7x) is (25x^2+39x-42)/(2sqrt(x+3))