What is the derivative of 4^{2x^2} ?

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

What is the first derivative of 4^{2x^2} ?

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

Popular >

derivative of

4^{2 x^{2}}

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

Solution steps

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

Simplify

4^{2 x^{2}} : 1 6^{x^{2}}

= \frac{d}{d x} (1 6^{x^{2}})

Apply exponent rule:

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

1 6^{x^{2}} = e^{x^{2} l n (16)}

= \frac{d}{d x} (e^{x^{2} l n (16)})

Apply the chain rule:

e^{x^{2} l n (16)} \frac{d}{d x} (x^{2} ln (16))

= e^{x^{2} l n (16)} \frac{d}{d x} (x^{2} ln (16))

\frac{d}{d x} (x^{2} ln (16)) = 8 ln (2) x

= e^{x^{2} l n (16)} \cdot 8 ln (2) x

Simplify

e^{x^{2} l n (16)} \cdot 8 ln (2) x : ln (2) \cdot 2^{4 x^{2} + 3} x

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

2 + 3 x

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

\frac{\partial}{\partial x} (- sin (x^{2} y) \cdot x^{2})

\frac{\partial}{\partial y} (\frac{( 3 x + y )}{z})

\frac{d}{d x} (4^{5 x})

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