What is the derivative of y=16^{sin(x^2)} ?

The derivative of y=16^{sin(x^2)} is ln(2)*2^{4sin(x^2)+3}xcos(x^2)

What is the first derivative of y=16^{sin(x^2)} ?

The first derivative of y=16^{sin(x^2)} is ln(2)*2^{4sin(x^2)+3}xcos(x^2)

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derivative of

y = 1 6^{s i n (x^{2})}

ln (2) \cdot 2^{4 s i n (x^{2}) + 3} x cos (x^{2})

Solution steps

\frac{d}{d x} (1 6^{s i n (x^{2})})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= ln (2) \cdot 2^{4 s i n (x^{2}) + 3} x cos (x^{2})

What is the derivative of y=16^{sin(x^2)} ?
The derivative of y=16^{sin(x^2)} is ln(2)*2^{4sin(x^2)+3}xcos(x^2)
What is the first derivative of y=16^{sin(x^2)} ?
The first derivative of y=16^{sin(x^2)} is ln(2)*2^{4sin(x^2)+3}xcos(x^2)