What is the derivative of sqrt(cos(2^x*x^5)) ?

The derivative of sqrt(cos(2^x*x^5)) is -2^{x-1}x^4sin(2^xx^5)sqrt(sec(2^xx^5))(ln(2)x+5)

What is the first derivative of sqrt(cos(2^x*x^5)) ?

The first derivative of sqrt(cos(2^x*x^5)) is -2^{x-1}x^4sin(2^xx^5)sqrt(sec(2^xx^5))(ln(2)x+5)

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\frac{d}{d x} (cos (2^{x} \cdot x^{5}))

- 2^{x - 1} x^{4} sin (2^{x} x^{5}) sec (2^{x} x^{5}) (ln (2) x + 5)

Solution steps

\frac{d}{d x} (cos (2^{x} x^{5}))

Apply the chain rule:

\frac{1}{2 cos ( 2 ^{x} x ^{5} )} \frac{d}{d x} (cos (2^{x} x^{5}))

= \frac{1}{2 cos ( 2 ^{x} x ^{5} )} \frac{d}{d x} (cos (2^{x} x^{5}))

\frac{d}{d x} (cos (2^{x} x^{5})) = - sin (2^{x} x^{5}) (2^{x} ln (2) x^{5} + 5 x^{4} \cdot 2^{x})

= \frac{1}{2 cos ( 2 ^{x} x ^{5} )} (- sin (2^{x} x^{5}) (2^{x} ln (2) x^{5} + 5 x^{4} \cdot 2^{x}))

Simplify

\frac{1}{2 cos ( 2 ^{x} x ^{5} )} (- sin (2^{x} x^{5}) (2^{x} ln (2) x^{5} + 5 x^{4} \cdot 2^{x})) : - 2^{x - 1} x^{4} sin (2^{x} x^{5}) sec (2^{x} x^{5}) (ln (2) x + 5)

= - 2^{x - 1} x^{4} sin (2^{x} x^{5}) sec (2^{x} x^{5}) (ln (2) x + 5)

\frac{d}{d x} (9 + 9 - x)

\int (15 x + 2) d x

x \to - 3 + lim (8 x + 5)

\int \frac{1}{4 y ^{2} + 1} d y

\frac{\partial}{\partial x} (x ln (1 + x + y))

What is the derivative of sqrt(cos(2^x*x^5)) ?
The derivative of sqrt(cos(2^x*x^5)) is -2^{x-1}x^4sin(2^xx^5)sqrt(sec(2^xx^5))(ln(2)x+5)
What is the first derivative of sqrt(cos(2^x*x^5)) ?
The first derivative of sqrt(cos(2^x*x^5)) is -2^{x-1}x^4sin(2^xx^5)sqrt(sec(2^xx^5))(ln(2)x+5)