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Differentiate a^x

Set y=a^x2. Take the natural log of both sides: ln(y)=ln(a^x)3. Using the log rules, simplify: ln(y)=xln(a)4. Differentiate both sides with respect to x: 1/y dy/dx=lna+05. Rearrange: dy/dx=yln(a)6. Using the...
HK
Answered by Hafsah K. • Maths tutor
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Find the tangent to the curve y=x^3+3 at the point x=1.

1. Differentiate the Equation of the curve to find the gradient: y'=3x^2 2. The gradient of the tangent is found by substituting x=1 into y'=3x^2: Gradient of tangent=3 3. Now we must find out the co-ordinat...
SK
Answered by Sevenia K. • Maths tutor
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Use the substition u = cos(x) to find the indefinite integral of -12sin(x)cos^3(x) dx

We are given the substitution to use, so the first step is to differentiate "u" with respect to x . du/dx = -sin(x) Now, to replace the "dx" in the original integrand with something in te...
AH
Answered by Arnab H. • Maths tutor
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Differentiate x^3(sinx) with respect to x

As we are differentiating a product (two things times together) we can use the product rule which is if: y = u(x)v(x) then dy/dx = u(dv/dx) + v(du/dx). So firstly looking at our equation we need to identify ...
SC
Answered by Sophie C. • Maths tutor
32603 Views

Find the integral between 4 and 1 of x^(3/2)-1 with respect to x

When we integrate a function we must first raise the power of x in each term by one. The first term therefore becomes x^(5/2). The second term can be thought of as x^0 which we know that any number to the po...
AB
Answered by Alex B. • Maths tutor
4856 Views