What is the derivative of y=(e^{4x}-3)^8 ?

The derivative of y=(e^{4x}-3)^8 is 32e^{4x}(e^{4x}-3)^7

What is the first derivative of y=(e^{4x}-3)^8 ?

The first derivative of y=(e^{4x}-3)^8 is 32e^{4x}(e^{4x}-3)^7

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derivative of

y = (e^{4 x} - 3)^{8}

32 e^{4 x} (e^{4 x} - 3)^{7}

Solution steps

\frac{d}{d x} ((e^{4 x} - 3)^{8})

Apply the chain rule:

8 (e^{4 x} - 3)^{7} \frac{d}{d x} (e^{4 x} - 3)

= 8 (e^{4 x} - 3)^{7} \frac{d}{d x} (e^{4 x} - 3)

\frac{d}{d x} (e^{4 x} - 3) = 4 e^{4 x}

= 8 (e^{4 x} - 3)^{7} \cdot 4 e^{4 x}

Simplify

= 32 e^{4 x} (e^{4 x} - 3)^{7}

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

x^{3} - 5 x, 4 x

\frac{d}{d x} (\frac{7}{x + 4})

d x - e^{3 x} d y = 0

\frac{\partial}{\partial x} (x^{6 y})

What is the derivative of y=(e^{4x}-3)^8 ?
The derivative of y=(e^{4x}-3)^8 is 32e^{4x}(e^{4x}-3)^7
What is the first derivative of y=(e^{4x}-3)^8 ?
The first derivative of y=(e^{4x}-3)^8 is 32e^{4x}(e^{4x}-3)^7