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Popular >

derivative of xsqrt(a+bx)

Solution

derivative of

x a + b x

Solution

\frac{3 b x + 2 a}{2 a + b x}

Solution steps

\frac{d}{d x} (x a + b x)

Apply the Product Rule:

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

f = x, g = a + b x

= \frac{d x}{d x} a + b x + \frac{d}{d x} (a + b x) x

\frac{d x}{d x} = 1

\frac{d}{d x} (a + b x) = \frac{b}{2 a + b x}

= 1 \cdot a + b x + \frac{b}{2 a + b x} x

Simplify

1 \cdot a + b x + \frac{b}{2 a + b x} x : \frac{3 b x + 2 a}{2 a + b x}

= \frac{3 b x + 2 a}{2 a + b x}

Popular Examples

integral of (ln(6x))/(x^4)

\int \frac{ln ( 6 x )}{x ^{4}} d x

integral from 1 to sqrt(2 of)x

\int_{1}^{2} x d x

(\partial)/(\partial z)(arctan(y/x))

\frac{\partial}{\partial z} (arctan (\frac{y}{x}))

integral of 1/(x^2*sqrt(9-x^2))

\int \frac{1}{x ^{2} \cdot 9 - x ^{2}} d x

integral of (x^2-x+10)/((x+2)(x^2+4))

\int \frac{x ^{2} - x + 10}{( x + 2 ) ( x ^{2} + 4 )} d x

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(a+bx) ?
The derivative of xsqrt(a+bx) is (3bx+2a)/(2sqrt(a+bx))
What is the first derivative of xsqrt(a+bx) ?
The first derivative of xsqrt(a+bx) is (3bx+2a)/(2sqrt(a+bx))