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Popular >

derivative of y=x^{2x+5}

Solution

derivative of

y = x^{2 x + 5}

Solution

x^{2 x + 5} (2 ln (x) + \frac{2 x + 5}{x})

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{2 x + 5} = e^{(2 x + 5) l n (x)}

= \frac{d}{d x} (e^{(2 x + 5) l n (x)})

Apply the chain rule:

e^{(2 x + 5) l n (x)} \frac{d}{d x} ((2 x + 5) ln (x))

= e^{(2 x + 5) l n (x)} \frac{d}{d x} ((2 x + 5) ln (x))

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

= e^{(2 x + 5) l n (x)} (2 ln (x) + \frac{2 x + 5}{x})

e^{(2 x + 5) l n (x)} = x^{2 x + 5}

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

Popular Examples

(\partial)/(\partial x)(ln(9-x^2-y^2))

\frac{\partial}{\partial x} (ln (9 - x^{2} - y^{2}))

(\partial)/(\partial z)(z(y-yz)^4)

\frac{\partial}{\partial z} (z (y - yz)^{4})

integral from 0 to 5 of e^{-x}

\int_{0}^{5} e^{- x} d x

(x^2+1)(dy)/(dx)+3x(y-1)=0,y(0)=3

(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0, y (0) = 3

(\partial)/(\partial x)(x^2+y^2+2/(xy))

\frac{\partial}{\partial x} (x^{2} + y^{2} + \frac{2}{x y})

Frequently Asked Questions (FAQ)

What is the derivative of y=x^{2x+5} ?
The derivative of y=x^{2x+5} is x^{2x+5}(2ln(x)+(2x+5)/x)
What is the first derivative of y=x^{2x+5} ?
The first derivative of y=x^{2x+5} is x^{2x+5}(2ln(x)+(2x+5)/x)