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Popular >

derivative of 1+3^{sin(x^3})

Solution

\frac{d}{d x} (1 + 3^{s i n (x^{3})})

Solution

ln (3) \cdot 3^{s i n (x^{3}) + 1} x^{2} cos (x^{3})

Solution steps

\frac{d}{d x} (1 + 3^{s i n (x^{3})})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) + \frac{d}{d x} (3^{s i n (x^{3})})

\frac{d}{d x} (1) = 0

\frac{d}{d x} (3^{s i n (x^{3})}) = ln (3) \cdot 3^{s i n (x^{3}) + 1} x^{2} cos (x^{3})

= 0 + ln (3) \cdot 3^{s i n (x^{3}) + 1} x^{2} cos (x^{3})

Simplify

= ln (3) \cdot 3^{s i n (x^{3}) + 1} x^{2} cos (x^{3})

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Frequently Asked Questions (FAQ)

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