What is the derivative of (4x)^{8x} ?

The derivative of (4x)^{8x} is ln(2)*2^{16x+4}x^{8x}+2^{3+16x}x^{8x}(ln(x)+1)

What is the first derivative of (4x)^{8x} ?

The first derivative of (4x)^{8x} is ln(2)*2^{16x+4}x^{8x}+2^{3+16x}x^{8x}(ln(x)+1)

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derivative of

(4 x)^{8 x}

ln (2) \cdot 2^{16 x + 4} x^{8 x} + 2^{3 + 16 x} x^{8 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} ((4 x)^{8 x})

Simplify

(4 x)^{8 x} : 6553 6^{x} x^{8 x}

= \frac{d}{d x} (6553 6^{x} x^{8 x})

Apply the Product Rule:

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

f = 6553 6^{x}, g = x^{8 x}

= \frac{d}{d x} (6553 6^{x}) x^{8 x} + \frac{d}{d x} (x^{8 x}) 6553 6^{x}

\frac{d}{d x} (6553 6^{x}) = ln (2) \cdot 2^{16 x + 4}

\frac{d}{d x} (x^{8 x}) = 8 x^{8 x} (ln (x) + 1)

= ln (2) \cdot 2^{16 x + 4} x^{8 x} + 8 x^{8 x} (ln (x) + 1) \cdot 6553 6^{x}

8 x^{8 x} (ln (x) + 1) \cdot 6553 6^{x} = 2^{3 + 16 x} x^{8 x} (ln (x) + 1)

= ln (2) \cdot 2^{16 x + 4} x^{8 x} + 2^{3 + 16 x} x^{8 x} (ln (x) + 1)

\frac{d}{d x} (\frac{5 x ^{3}}{4} - \frac{2}{5 x ^{3}})

f (x) = e^{7 x}

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

\int (\frac{( x ^{m} - x ^{n} ) ^{2}}{x}) d x

\frac{\partial}{\partial y} (4 x^{2} + 2 x y + y^{2} - 8)

What is the derivative of (4x)^{8x} ?
The derivative of (4x)^{8x} is ln(2)*2^{16x+4}x^{8x}+2^{3+16x}x^{8x}(ln(x)+1)
What is the first derivative of (4x)^{8x} ?
The first derivative of (4x)^{8x} is ln(2)*2^{16x+4}x^{8x}+2^{3+16x}x^{8x}(ln(x)+1)