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Popular >

d/(d{z)}({x}^{{y}^{{z}}})

Solution

\frac{d}{d z} (x^{y^{z}})

Solution

ln (x) ln (y) x^{y^{z}} y^{z}

Solution steps

\frac{d}{d z} (x^{y^{z}})

Apply exponent rule:

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

x^{y^{z}} = e^{y^{z} l n (x)}

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

Apply the chain rule:

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

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

\frac{d}{d z} (y^{z} ln (x)) = ln (x) y^{z} ln (y)

= e^{y^{z} l n (x)} ln (x) y^{z} ln (y)

e^{y^{z} l n (x)} = x^{y^{z}}

= ln (x) ln (y) x^{y^{z}} y^{z}

Popular Examples

sum from n=0 to infinity of 1-(0.2)^n

n = 0 \sum \infty 1 - (0.2)^{n}

derivative of e^{-6x}sin(6x)

\frac{d}{d x} (e^{- 6 x} sin (6 x))

integral of y/(sqrt(1-4y^4))

\int \frac{y}{1 - 4 y ^{4}} d y

derivative of 4x^{-2x}

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

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

Frequently Asked Questions (FAQ)

What is the d/(d{z)}({x}^{{y}^{{z}}}) ?
The d/(d{z)}({x}^{{y}^{{z}}}) is ln({x})ln({y}){x}^{{y}^{{z}}}{y}^{{z}}
What is the first d/(d{z)}({x}^{{y}^{{z}}}) ?
The first d/(d{z)}({x}^{{y}^{{z}}}) is ln({x})ln({y}){x}^{{y}^{{z}}}{y}^{{z}}