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Popular >

derivative of 2^x(pix^2+cos(x))

Solution

\frac{d}{d x} (2^{x} (π x^{2} + cos (x)))

Solution

2^{x} ln (2) (π x^{2} + cos (x)) + (2 π x - sin (x)) \cdot 2^{x}

Solution steps

\frac{d}{d x} (2^{x} (π x^{2} + cos (x)))

Apply the Product Rule:

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

f = 2^{x}, g = π x^{2} + cos (x)

= \frac{d}{d x} (2^{x}) (π x^{2} + cos (x)) + \frac{d}{d x} (π x^{2} + cos (x)) 2^{x}

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

\frac{d}{d x} (π x^{2} + cos (x)) = 2 π x - sin (x)

= 2^{x} ln (2) (π x^{2} + cos (x)) + (2 π x - sin (x)) \cdot 2^{x}

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Frequently Asked Questions (FAQ)

What is the derivative of 2^x(pix^2+cos(x)) ?
The derivative of 2^x(pix^2+cos(x)) is 2^xln(2)(pix^2+cos(x))+(2pix-sin(x))*2^x
What is the first derivative of 2^x(pix^2+cos(x)) ?
The first derivative of 2^x(pix^2+cos(x)) is 2^xln(2)(pix^2+cos(x))+(2pix-sin(x))*2^x