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Popular >

derivative of 2^xtan(3x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2^{x}, g = tan (3 x)

= \frac{d}{d x} (2^{x}) tan (3 x) + \frac{d}{d x} (tan (3 x)) 2^{x}

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

\frac{d}{d x} (tan (3 x)) = sec^{2} (3 x) \cdot 3

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

Popular Examples

(\partial)/(\partial z)(xy+2z)

\frac{\partial}{\partial z} (x y + 2 z)

(\partial)/(\partial x)(5xy-18x)

\frac{\partial}{\partial x} (5 x y - 18 x)

derivative of (7x+8(8x-9))

\frac{d}{d x} ((7 x + 8) (8 x - 9))

integral of (sqrt(x^2-225))/x

\int \frac{x ^{2} - 225}{x} d x

y^'=2xsqrt(1-y^2)

y^{^{'}} = 2 x 1 - y^{2}

Frequently Asked Questions (FAQ)

What is the derivative of 2^xtan(3x) ?
The derivative of 2^xtan(3x) is 2^xln(2)tan(3x)+sec^2(3x)*3*2^x
What is the first derivative of 2^xtan(3x) ?
The first derivative of 2^xtan(3x) is 2^xln(2)tan(3x)+sec^2(3x)*3*2^x