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Popular >

derivative of x^{6x}

Solution

derivative of

x^{6 x}

Solution

6 x^{6 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{6 x})

Apply exponent rule:

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

x^{6 x} = e^{6 x l n (x)}

= \frac{d}{d x} (e^{6 x l n (x)})

Apply the chain rule:

e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

= e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

\frac{d}{d x} (6 x ln (x)) = 6 (ln (x) + 1)

= e^{6 x l n (x)} \cdot 6 (ln (x) + 1)

e^{6 x l n (x)} = x^{6 x}

= 6 x^{6 x} (ln (x) + 1)

Popular Examples

derivative of (x^3)/3+x^2+4x-10 derivative of

\frac{x ^{3}}{3} + x^{2} + 4 x - 10

derivative of (3x^2/((x^2+x)^3))

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

area 17e^{0.02t},21e^{0.02t},[0,50]area

17 e^{0.02 t}, 21 e^{0.02 t}, [0, 50]

(\partial)/(\partial y)(xcos(y))

\frac{\partial}{\partial y} (x cos (y))

(dy)/(dx)=3x^2y

\frac{d y}{d x} = 3 x^{2} y

Frequently Asked Questions (FAQ)

What is the derivative of x^{6x} ?
The derivative of x^{6x} is 6x^{6x}(ln(x)+1)
What is the first derivative of x^{6x} ?
The first derivative of x^{6x} is 6x^{6x}(ln(x)+1)