What is the derivative of 2^zlog_{2}(z) ?

The derivative of 2^zlog_{2}(z) is 2^zln(z)+(2^z)/(ln(2)z)

What is the first derivative of 2^zlog_{2}(z) ?

The first derivative of 2^zlog_{2}(z) is 2^zln(z)+(2^z)/(ln(2)z)

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derivative of

2^{z} lo g_{2} (z)

2^{z} ln (z) + \frac{2 ^{z}}{ln ( 2 ) z}

Solution steps

\frac{d}{d z} (2^{z} lo g_{2} (z))

Apply the Product Rule:

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

f = 2^{z}, g = lo g_{2} (z)

= \frac{d}{d z} (2^{z}) lo g_{2} (z) + \frac{d}{d z} (lo g_{2} (z)) 2^{z}

\frac{d}{d z} (2^{z}) = 2^{z} ln (2)

\frac{d}{d z} (lo g_{2} (z)) = \frac{1}{z ln ( 2 )}

= 2^{z} ln (2) lo g_{2} (z) + \frac{1}{z ln ( 2 )} \cdot 2^{z}

Simplify

2^{z} ln (2) lo g_{2} (z) + \frac{1}{z ln ( 2 )} \cdot 2^{z} : 2^{z} ln (z) + \frac{2 ^{z}}{ln ( 2 ) z}

= 2^{z} ln (z) + \frac{2 ^{z}}{ln ( 2 ) z}

y^{^{'}} + (\frac{3 y}{( 300 - t )}) = 4

\int \frac{64 x ^{2} - 1}{x} d x

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

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

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 6)

What is the derivative of 2^zlog_{2}(z) ?
The derivative of 2^zlog_{2}(z) is 2^zln(z)+(2^z)/(ln(2)z)
What is the first derivative of 2^zlog_{2}(z) ?
The first derivative of 2^zlog_{2}(z) is 2^zln(z)+(2^z)/(ln(2)z)