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Popular >

derivative of y=x^{mx}

Solution

derivative of

y = x^{m x}

Solution

m x^{m x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{m x})

Apply exponent rule:

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

x^{m x} = e^{m x l n (x)}

= \frac{d}{d x} (e^{m x l n (x)})

Apply the chain rule:

e^{m x l n (x)} \frac{d}{d x} (m x ln (x))

= e^{m x l n (x)} \frac{d}{d x} (m x ln (x))

\frac{d}{d x} (m x ln (x)) = m (ln (x) + 1)

= e^{m x l n (x)} m (ln (x) + 1)

e^{m x l n (x)} = x^{m x}

= m x^{m x} (ln (x) + 1)

Popular Examples

(\partial)/(\partial x)(y^2+2e^{x^2}xy)

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

integral of (ln(x^2))/2

\int \frac{ln ( x ^{2} )}{2} d x

taylor x^3+8x-1,-1 taylor

x^{3} + 8 x - 1, - 1

(\partial)/(\partial y)(sqrt(29-x^2-4y^2))

\frac{\partial}{\partial y} (29 - x^{2} - 4 y^{2})

derivative of 4^xlog_{4}(x)

\frac{d}{d x} (4^{x} lo g_{4} (x))

Frequently Asked Questions (FAQ)

What is the derivative of y=x^{mx} ?
The derivative of y=x^{mx} is mx^{mx}(ln(x)+1)
What is the first derivative of y=x^{mx} ?
The first derivative of y=x^{mx} is mx^{mx}(ln(x)+1)